{"id":119196,"date":"2026-10-29T02:48:30","date_gmt":"2026-10-28T18:48:30","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/119196.html"},"modified":"2026-10-29T02:48:30","modified_gmt":"2026-10-28T18:48:30","slug":"swe-%e7%9a%84%e5%8e%9f%e7%90%86%e8%a7%a3%e6%9e%90","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/119196.html","title":{"rendered":"SWE \u7684\u539f\u7406\u89e3\u6790"},"content":{"rendered":"

\u4e8c\u3001SWE \u7684\u8fd0\u52a8\u673a\u5236<\/h3>\n

SWE \u7684\u8fd0\u52a8\u673a\u5236\u53ef\u4ee5\u7406\u89e3\u6210：\u6c34\u9762\u5761\u5ea6\u6539\u53d8\u6d41\u901f，\u6d41\u52a8\u7684\u6c47\u805a\u548c\u53d1\u6563\u6539\u53d8\u6c34\u6df1\u3002<\/p>\n

\u5047\u8bbe\u4f60\u5728\u5e73\u9759\u6c34\u9762\u4e2d\u592e\u5236\u9020\u4e00\u4e2a\u9686\u8d77：<\/p>\n

  • \u4e2d\u592e\u4e0e\u5468\u56f4\u51fa\u73b0\u6c34\u9762\u9ad8\u5ea6\u5dee\u3002<\/li>\n
  • \u9ad8\u5ea6\u5dee\u4ea7\u751f\u6c34\u5e73\u538b\u529b\u68af\u5ea6，\u4f7f\u6c34\u5411\u5468\u56f4\u52a0\u901f\u3002<\/li>\n
  • \u4e2d\u592e\u6d41\u51fa\u7684\u6c34\u591a，\u6c34\u9762\u4e0b\u964d；\u5468\u56f4\u5f97\u5230\u6c34，\u6c34\u9762\u4e0a\u5347\u3002<\/li>\n
  • \u5f53\u6c34\u9762\u6682\u65f6\u53d8\u5e73\u65f6，\u6c34\u4ecd\u7136\u5177\u6709\u901f\u5ea6\u3002<\/li>\n
  • \u6c34\u7ee7\u7eed\u8fd0\u52a8，\u4ea7\u751f\u65b0\u7684\u51f9\u9677\u548c\u9686\u8d77，\u6270\u52a8\u7531\u6b64\u5411\u5916\u4f20\u64ad\u3002<\/li>\n

    \u6240\u4ee5，SWE \u9700\u8981\u540c\u65f6\u4fdd\u5b58\u201c\u6c34\u6709\u591a\u5c11\u201d\u548c\u201c\u6c34\u5982\u4f55\u8fd0\u52a8\u201d\u3002<\/p>\n

    \u8fd9\u4e5f\u89e3\u91ca\u4e86\u4e3a\u4ec0\u4e48：\u4ec5\u6839\u636e\u5f53\u524d\u9ad8\u5ea6\u56fe，\u901a\u5e38\u4e0d\u80fd\u552f\u4e00\u51b3\u5b9a\u4e0b\u4e00\u65f6\u523b\u7684\u6c34\u9762\u3002 \u4e24\u7247\u5f62\u72b6\u5b8c\u5168\u76f8\u540c\u7684\u6c34\u9762，\u53ef\u80fd\u4e00\u4e2a\u6b63\u5728\u5411\u5916\u6d41\u52a8，\u53e6\u4e00\u4e2a\u6b63\u5728\u5411\u5185\u6c47\u805a，\u5b83\u4eec\u4e0b\u4e00\u523b\u7684\u53d8\u5316\u4f1a\u4e0d\u540c\u3002<\/p>\n

    1\u3001\u8d28\u91cf\u5b88\u6052<\/h4>\n

    \u5bf9\u4e8e\u5bc6\u5ea6\u6052\u5b9a\u7684\u6c34，\u8d28\u91cf\u5b88\u6052\u7b49\u4ef7\u4e8e\u4f53\u79ef\u5b88\u6052\u3002<\/p>\n

    \u4e0d\u53ef\u538b\u7f29\u6d41\u4f53\u7684\u4e09\u7ef4\u8fde\u7eed\u6027\u65b9\u7a0b（\u6563\u5ea6\u5f62\u5f0f）：<\/p>\n

    \u2202u\u2202x+\u2202w\u2202y+\u2202v\u2202z=0
    \n\\\\frac{\\\\partial u}{\\\\partial x} + \\\\frac{\\\\partial w}{\\\\partial y} + \\\\frac{\\\\partial v}{\\\\partial z} = 0
    \n<\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>y<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>w<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u8003\u8651\u6c34\u5e73\u9762\u79ef\u4e3a A \u7684\u4e00\u4e2a\u7f51\u683c\u5355\u5143，\u5185\u90e8\u6c34\u7684\u4f53\u79ef\u4e3a：<\/p>\n

    V=Ah
    \nV = Ah
    \n<\/span><\/span>V<\/span><\/span>=<\/span><\/span><\/span><\/span>A<\/span>h<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u82e5\u6d41\u5165\u3001\u6d41\u51fa\u7684\u4f53\u79ef\u6d41\u91cf\u5206\u522b\u4e3a Qin\u3001Qout，\u90a3\u4e48：<\/p>\n

    dVdt=Qin\u2212Qout
    \n\\\\frac{dV}{dt} = Q_{in} – Q_{out}
    \n<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>V<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>Q<\/span><\/span>in<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>Q<\/span><\/span>o<\/span>u<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u56e0\u6b64：<\/p>\n

    dhdt=Qin\u2212QoutA
    \n\\\\frac{dh}{dt} = \\\\frac{Q_{in} – Q_{out}}{A}
    \n<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>h<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>A<\/span><\/span><\/span><\/span><\/span><\/span><\/span>Q<\/span><\/span>in<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>Q<\/span><\/span>o<\/span>u<\/span>t<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u4f8b\u5982，\u9762\u79ef\u4e3a1m^2\u7684\u5355\u5143，\u6bcf\u79d2\u6d41\u5165 0.03m^3\u3001\u6d41\u51fa 0.01m^3，\u6c34\u6df1\u5c31\u6bcf\u79d2\u589e\u52a0 0.02m\u3002<\/p>\n

    \u628a\u8fd9\u4e2a\u5173\u7cfb\u5199\u6210\u8fde\u7eed\u7a7a\u95f4\u4e2d\u7684\u65b9\u7a0b：<\/p>\n

    \u2202h\u2202t+\u2202(hu)\u2202x+\u2202(hv)\u2202z=0
    \n\\\\frac{\\\\partial h}{\\\\partial t} + \\\\frac{\\\\partial(hu)}{\\\\partial x} + \\\\frac{\\\\partial(hv)}{\\\\partial z} = 0
    \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>h<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>u<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>v<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u5176\u4e2d：<\/p>\n

      \n
    • hu：\u6cbf x \u65b9\u5411\u7684\u5355\u4f4d\u5bbd\u5ea6\u4f53\u79ef\u6d41\u91cf；<\/li>\n
    • hv：\u6cbf z \u65b9\u5411\u7684\u5355\u4f4d\u5bbd\u5ea6\u4f53\u79ef\u6d41\u91cf；<\/li>\n
    • \u540e\u4e24\u9879\u4e4b\u548c：\u4e00\u4e2a\u4f4d\u7f6e\u9644\u8fd1\u51c0\u6d41\u51fa\u7684\u7a0b\u5ea6\u3002<\/li>\n<\/ul>\n

      \u51c0\u6d41\u51fa\u4e3a\u6b63，\u6c34\u6df1\u4e0b\u964d；\u51c0\u6d41\u5165\u4e3a\u6b63，\u6c34\u6df1\u4e0a\u5347\u3002\u8fd9\u5c31\u662f\u6ca1\u6709\u5916\u90e8\u6c34\u6e90\u65f6\u7684\u8fde\u7eed\u6027\u65b9\u7a0b\u3002<\/p>\n

      \u5c55\u5f00\u53ef\u4ee5\u5f97\u5230：<\/p>\n

      \u2202h\u2202t+u\u2202h\u2202x+v\u2202h\u2202z=\u2212h(\u2202u\u2202x+\u2202v\u2202z)
      \n\\\\frac{\\\\partial h}{\\\\partial t} + u\\\\frac{\\\\partial h}{\\\\partial x} + v\\\\frac{\\\\partial h}{\\\\partial z} = -h\\\\left( \\\\frac{\\\\partial u}{\\\\partial x} + \\\\frac{\\\\partial v}{\\\\partial z} \\\\right)
      \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>h<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>u<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>h<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>v<\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>h<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>h<\/span><\/span>(<\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u53f3\u4fa7\u62ec\u53f7\u5185\u662f\u6c34\u5e73\u901f\u5ea6\u7684\u6563\u5ea6：<\/p>\n

      \u2207\u22c5u=\u2202u\u2202x+\u2202v\u2202z
      \n\\\\nabla\\\\cdot\\\\boldsymbol{u} = \\\\frac{\\\\partial u}{\\\\partial x} + \\\\frac{\\\\partial v}{\\\\partial z}
      \n<\/span><\/span>\u2207<\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>u<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

      \u8ddf\u968f\u6c34\u6d41\u89c2\u5bdf\u65f6：<\/p>\n

        \n
      • \u901f\u5ea6\u573a\u5411\u5916\u53d1\u6563，\u6c34\u67f1\u88ab\u644a\u5f00，\u6c34\u6df1\u51cf\u5c0f；<\/li>\n
      • \u901f\u5ea6\u573a\u5411\u5185\u6c47\u805a，\u6c34\u88ab\u5806\u79ef，\u6c34\u6df1\u589e\u5927\u3002<\/li>\n<\/ul>\n

        \u6c34\u672c\u8eab\u6ca1\u6709\u88ab\u538b\u7f29，\u6539\u53d8\u7684\u662f\u6c34\u67f1\u7684\u5f62\u72b6\u3002<\/p>\n

        2\u3001\u6c34\u5e73\u52a8\u91cf\u65b9\u7a0b<\/h4>\n

        \u53e6\u5916\u4e24\u6761\u6838\u5fc3\u65b9\u7a0b\u662f\u6c34\u5e73\u52a8\u91cf\u65b9\u7a0b，\u5b83\u4eec\u51b3\u5b9a\u6d41\u901f\u600e\u6837\u53d8\u5316\u3002<\/p>\n

        \u5148\u8003\u8651\u56fa\u5b9a\u5e95\u5e8a，\u5e76\u5ffd\u7565\u6469\u64e6\u3001\u98ce\u529b\u548c\u5730\u7403\u81ea\u8f6c：<\/p>\n

        \u2202u\u2202t+u\u2202u\u2202x+v\u2202u\u2202z=\u2212g\u2202\u03b7\u2202x
        \n\\\\frac{\\\\partial u}{\\\\partial t} + u\\\\frac{\\\\partial u}{\\\\partial x} + v\\\\frac{\\\\partial u}{\\\\partial z} = -g\\\\frac{\\\\partial\\\\eta}{\\\\partial x}
        \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>u<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>v<\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        \u2202v\u2202t+u\u2202v\u2202x+v\u2202v\u2202z=\u2212g\u2202\u03b7\u2202x
        \n\\\\frac{\\\\partial v}{\\\\partial t} + u\\\\frac{\\\\partial v}{\\\\partial x} + v\\\\frac{\\\\partial v}{\\\\partial z} = -g\\\\frac{\\\\partial\\\\eta}{\\\\partial x}
        \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>u<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>v<\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        \u8fd9\u4e24\u6761\u5f0f\u5b50\u7ed3\u6784\u76f8\u540c，\u53ea\u662f\u5206\u522b\u63cf\u8ff0\u4e24\u4e2a\u6c34\u5e73\u65b9\u5411\u3002<\/p>\n

        \u2202u\u2202t\u23df\u56fa\u5b9a\u4f4d\u7f6e\u7684\u6d41\u901f\u53d8\u5316+u\u2202u\u2202x+v\u2202u\u2202z\u23df\u6d41\u52a8\u5e26\u6765\u7684\u5bf9\u6d41\u52a0\u901f\u5ea6=\u2212g\u2202\u03b7\u2202x\u23df\u6c34\u9762\u5761\u5ea6\u5f15\u8d77\u7684\u52a0\u901f\u5ea6
        \n\\\\underbrace{\\\\frac{\\\\partial u}{\\\\partial t}}_{\\\\text{\u56fa\u5b9a\u4f4d\u7f6e\u7684\u6d41\u901f\u53d8\u5316}} + \\\\underbrace{ u\\\\frac{\\\\partial u}{\\\\partial x} + v\\\\frac{\\\\partial u}{\\\\partial z} }_{\\\\text{\u6d41\u52a8\u5e26\u6765\u7684\u5bf9\u6d41\u52a0\u901f\u5ea6}} = \\\\underbrace{ -g\\\\frac{\\\\partial\\\\eta}{\\\\partial x} }_{\\\\text{\u6c34\u9762\u5761\u5ea6\u5f15\u8d77\u7684\u52a0\u901f\u5ea6}}
        \n<\/span><\/span><\/span>\u56fa\u5b9a\u4f4d\u7f6e\u7684\u6d41\u901f\u53d8\u5316<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span>\u6d41\u52a8\u5e26\u6765\u7684\u5bf9\u6d41\u52a0\u901f\u5ea6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>u<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>v<\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>\u6c34\u9762\u5761\u5ea6\u5f15\u8d77\u7684\u52a0\u901f\u5ea6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        \u201c\u5bf9\u6d41\u52a0\u901f\u5ea6\u201d\u53ef\u4ee5\u8fd9\u6837\u7406\u89e3：\u6c34\u6d41\u5230\u4e86\u53e6\u4e00\u4e2a\u901f\u5ea6\u4e0d\u540c\u7684\u4f4d\u7f6e，\u8ddf\u968f\u8fd9\u56e2\u6c34\u89c2\u5bdf，\u5b83\u7684\u901f\u5ea6\u5c31\u4f1a\u53d1\u751f\u53d8\u5316\u3002<\/p>\n

        \u53f3\u8fb9\u7684\u8d1f\u53f7\u8868\u793a，\u91cd\u529b\u6240\u4ea7\u751f\u7684\u538b\u529b\u4f5c\u7528\u4f1a\u4f7f\u6c34\u6cbf\u6c34\u9762\u964d\u4f4e\u7684\u65b9\u5411\u52a0\u901f\u3002\u6c34\u9762\u5761\u5ea6\u51b3\u5b9a\u7684\u662f\u52a0\u901f\u5ea6，\u800c\u4e0d\u662f\u76f4\u63a5\u51b3\u5b9a\u901f\u5ea6\u3002 \u56e0\u6b64，\u6c34\u9762\u521a\u53d8\u5e73\u65f6，\u6c34\u4ecd\u7136\u53ef\u80fd\u7ee7\u7eed\u6d41\u52a8\u3002<\/p>\n

        \u538b\u529b\u9879\u7684\u6765\u6e90\u4e5f\u5f88\u76f4\u89c2\u3002\u9759\u6c34\u538b\u529b\u8fd1\u4f3c\u4e3a：<\/p>\n

        p=\u03c1g(\u03b7\u2212Y)
        \np=\\\\rho g(\\\\eta-Y)
        \n<\/span><\/span>p<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03c1<\/span>g<\/span>(<\/span>\u03b7<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>Y<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        \u8fd9\u91cc\u4f7f\u7528\u76f8\u5bf9\u4e8e\u5927\u6c14\u538b\u7684\u538b\u529b\u3002\u5728\u76f8\u540c\u7ad6\u76f4\u9ad8\u5ea6 Y \u4e0a，\u6c34\u9762\u8d8a\u9ad8，\u4e0a\u65b9\u538b\u7740\u7684\u6c34\u8d8a\u591a，\u538b\u529b\u8d8a\u5927：<\/p>\n

        \u22121\u03c1\u2202p\u2202x=\u2212g\u2202\u03b7\u2202x
        \n-\\\\frac{1}{\\\\rho}\\\\frac{\\\\partial p}{\\\\partial x} = -g\\\\frac{\\\\partial\\\\eta}{\\\\partial x}
        \n<\/span><\/span>\u2212<\/span><\/span><\/span>\u03c1<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        \u8fd9\u5c31\u5f97\u5230\u4e86\u52a8\u91cf\u65b9\u7a0b\u4e2d\u7684\u9a71\u52a8\u529b\u3002<\/p>\n

        2.1 \u52a8\u91cf<\/h5>\n

        \u52a8\u91cf（Momentum）：\u662f\u6d41\u4f53\u5e26\u6709\u7684\u201c\u8fd0\u52a8\u7684\u529b\u91cf\u201d\u3002<\/p>\n

        p=mv
        \np = mv
        \n<\/span><\/span>p<\/span><\/span>=<\/span><\/span><\/span><\/span>m<\/span>v<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        2.2 \u52a8\u91cf\u901a\u91cf<\/h5>\n

        \u901a\u91cf（Flux）：\u200b\u5355\u4f4d\u65f6\u95f4\u5185，\u5782\u76f4\u7a7f\u8fc7\u5355\u4f4d\u9762\u79ef\u7684\u67d0\u79cd\u7269\u7406\u91cf\u200b\u3002<\/p>\n

        \u52a8\u91cf\u901a\u91cf（Momentum Flux）\u5c31\u662f\u6307：\u5355\u4f4d\u65f6\u95f4\u5185，\u901a\u8fc7\u5355\u4f4d\u9762\u79ef\u7684\u52a8\u91cf\u3002<\/p>\n

        \u52a8\u91cf\u901a\u91cf=\u03c1u\u2297u
        \n\u52a8\u91cf\u901a\u91cf = \\\\rho u \u2297 u
        \n<\/span><\/span>\u52a8\u91cf\u901a\u91cf<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03c1<\/span>u<\/span><\/span>\u2297<\/span><\/span><\/span><\/span>u<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        \u5176\u4e2d \u03c1 \u662f\u5bc6\u5ea6，u \u662f\u901f\u5ea6\u77e2\u91cf，\u2297 \u662f\u5f20\u91cf\u79ef\u3002<\/p>\n

        \u5982\u679c\u628a\u5b83\u5c55\u5f00，\u5728\u4e8c\u7ef4（x, z \u5e73\u9762）\u7684\u6d45\u6c34\u65b9\u7a0b\u4e2d，\u52a8\u91cf\u901a\u91cf\u5f20\u91cf\u5927\u6982\u957f\u8fd9\u6837：<\/p>\n

        [\u03c1u2\u03c1uw\u03c1wu\u03c1w2]
        \n\\\\begin{bmatrix}
        \n\\\\rho u^2 & \\\\rho uw \\\\\\\\
        \n\\\\rho wu & \\\\rho w^2
        \n\\\\end{bmatrix}
        \n<\/span><\/span>[<\/span><\/span><\/span>\u03c1<\/span>u<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c1w<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c1<\/span>u<\/span>w<\/span><\/span><\/span><\/span>\u03c1<\/span>w<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \n
        • \u5bf9\u89d2\u7ebf\u4e0a\u7684 \u03c1u\u00b2 \u548c \u03c1w\u00b2 \u53eb\u505a\u200b\u6b63\u5e94\u529b\u200b（\u76f8\u5f53\u4e8e\u6c34\u6d41\u52a8\u5e26\u6765\u7684\u52a8\u538b）\u3002<\/li>\n
        • \u975e\u5bf9\u89d2\u7ebf\u4e0a\u7684 \u03c1uw \u53eb\u505a\u200b\u526a\u5e94\u529b\u200b（\u4e0d\u540c\u65b9\u5411\u6c34\u6d41\u4ea4\u9519\u6469\u64e6\u3001\u62c9\u626f\u5e26\u6765\u7684\u529b）\u3002<\/li>\n<\/ul>\n
          2.3 \u4e09\u7ef4 N-S \u65b9\u7a0b<\/h5>\n

          \u5bf9\u4e8e\u4e0d\u53ef\u538b\u7f29\u3001\u65e0\u7c98\u6027\u7684\u6d41\u4f53，\u4e09\u7ef4 N-S \u65b9\u7a0b\u5728 xx \u65b9\u5411\u7684\u52a8\u91cf\u65b9\u7a0b\u4e3a：<\/p>\n

          \u2202u\u2202t+u\u2202u\u2202x+v\u2202u\u2202y+w\u2202u\u2202z=\u22121\u03c1\u2202p\u2202x+fx
          \n\\\\frac{\\\\partial u}{\\\\partial t} + u\\\\frac{\\\\partial u}{\\\\partial x} + v\\\\frac{\\\\partial u}{\\\\partial y} + w\\\\frac{\\\\partial u}{\\\\partial z} = -\\\\frac{1}{\\\\rho}\\\\frac{\\\\partial p}{\\\\partial x} + f\\\\mathrm{x}
          \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>u<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>v<\/span><\/span><\/span>\u2202<\/span>y<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>w<\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>\u03c1<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>f<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u5176\u4e2d u, v, w \u5206\u522b\u662f x, y, z \u65b9\u5411\u7684\u901f\u5ea6， y \u662f\u7ad6\u76f4\u65b9\u5411，p \u662f\u538b\u5f3a, fx \u662f\u5916\u529b\u3002<\/p>\n

          \u200b2.4 x \u200b\u65b9\u5411\u52a8\u91cf\u5b88\u6052\u65b9\u7a0b\u3002<\/h5>\n
          2.4.1 \u4ece\u4e09\u7ef4N-S\u65b9\u7a0b\u51fa\u53d1(x\u65b9\u5411)<\/h6>\n

          \u5229\u7528\u8fde\u7eed\u6027\u65b9\u7a0b（\u8d28\u91cf\u5b88\u6052\u7684\u6563\u5ea6\u5f62\u5f0f），\u6211\u4eec\u53ef\u4ee5\u5c06\u5de6\u8fb9\u7684\u5bf9\u6d41\u9879（\u975e\u7ebf\u6027\u9879）\u6539\u5199\u4e3a\u200b\u5b88\u6052\u5f62\u5f0f\u200b（Flux form，\u628a\u6240\u6709\u4e1c\u897f\u90fd\u585e\u8fdb\u504f\u5bfc\u6570\u91cc\u9762\u7684\u5f62\u5f0f）：<\/p>\n

          \u2202u\u2202x+\u2202v\u2202y+\u2202w\u2202z=0
          \n\\\\frac{\\\\partial u}{\\\\partial x} + \\\\frac{\\\\partial v}{\\\\partial y} + \\\\frac{\\\\partial w}{\\\\partial z} = 0
          \n<\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>y<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>w<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u4ee3\u5165 N-S \u65b9\u7a0b：<\/p>\n

          \u2202u\u2202t+u\u2202u\u2202x+v\u2202u\u2202y+w\u2202u\u2202z+u(\u2202u\u2202x+\u2202v\u2202y+\u2202w\u2202z)=\u22121\u03c1\u2202p\u2202x+fx
          \n\\\\frac{\\\\partial u}{\\\\partial t} + u\\\\frac{\\\\partial u}{\\\\partial x} + v\\\\frac{\\\\partial u}{\\\\partial y} + w\\\\frac{\\\\partial u}{\\\\partial z} + u(\\\\frac{\\\\partial u}{\\\\partial x} + \\\\frac{\\\\partial v}{\\\\partial y} + \\\\frac{\\\\partial w}{\\\\partial z}) = -\\\\frac{1}{\\\\rho}\\\\frac{\\\\partial p}{\\\\partial x} + f\\\\mathrm{x}
          \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>u<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>v<\/span><\/span><\/span>\u2202<\/span>y<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>w<\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>u<\/span>(<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>y<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>w<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>\u03c1<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>f<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u2202u\u2202t+2u\u2202u\u2202x+(v\u2202u\u2202y+u\u2202v\u2202y)+(w\u2202u\u2202z+u\u2202w\u2202z)=\u22121\u03c1\u2202p\u2202x+fx
          \n\\\\frac{\\\\partial u}{\\\\partial t} + 2u\\\\frac{\\\\partial u}{\\\\partial x} + (v\\\\frac{\\\\partial u}{\\\\partial y} + u\\\\frac{\\\\partial v}{\\\\partial y}) + (w\\\\frac{\\\\partial u}{\\\\partial z} + u\\\\frac{\\\\partial w}{\\\\partial z}) = -\\\\frac{1}{\\\\rho}\\\\frac{\\\\partial p}{\\\\partial x} + f\\\\mathrm{x}
          \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span>u<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>(<\/span>v<\/span><\/span><\/span>\u2202<\/span>y<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>u<\/span><\/span><\/span>\u2202<\/span>y<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span>(<\/span>w<\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>u<\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>w<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>\u03c1<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>f<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u6574\u7406\u5f97：<\/p>\n

          \u2202u\u2202t+\u2202u2\u2202x+\u2202uv\u2202y+\u2202uw\u2202z=\u22121\u03c1\u2202p\u2202x+fx
          \n\\\\frac{\\\\partial u}{\\\\partial t} + \\\\frac{\\\\partial u^2}{\\\\partial x} + \\\\frac{\\\\partial uv}{\\\\partial y} + \\\\frac{\\\\partial uw}{\\\\partial z} = -\\\\frac{1}{\\\\rho}\\\\frac{\\\\partial p}{\\\\partial x} + f\\\\mathrm{x}
          \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>y<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>uv<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span>w<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>\u03c1<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>f<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          2.4.2 \u6cbf\u6c34\u6df1 y \u65b9\u5411\u79ef\u5206<\/h6>\n

          \u7531\u4e8e\u6d45\u6c34\u65b9\u7a0b\u5f97\u6838\u5fc3\u5047\u8bbe\u662f：\u6c34\u5e73\u5c3a\u5ea6\u8fdc\u5927\u4e8e\u5782\u76f4\u5c3a\u5ea6，\u90a3\u4e48\u6211\u4eec\u5047\u8bbe\u5782\u76f4\u65b9\u5411\u7684\u52a0\u901f\u5ea6\u53ef\u4ee5\u5ffd\u7565\u4e0d\u8bb0，\u90a3\u4e48\u6709：<\/p>\n

          v\u2202u\u2202y\u2248u\u2202v\u2202y\u22480
          \nv\\\\frac{\\\\partial u}{\\\\partial y} \\\\approx u\\\\frac{\\\\partial v}{\\\\partial y} \\\\approx0
          \n<\/span><\/span>v<\/span><\/span><\/span>\u2202<\/span>y<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>u<\/span><\/span><\/span>\u2202<\/span>y<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>v<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u5c06\u4e0a\u8ff0\u65b9\u7a0b\u4ece\u6c34\u5e95 b(x, z)\u79ef\u5206\u5230\u6c34\u9762 \u03b7(x,z,t)：<\/p>\n

          \u222bb\u03b7\u2202u\u2202tdy=\u2202\u2202t\u222bb\u03b7udy=\u2202hu\u2202t
          \n\\\\int_{b}^{\\\\eta} \\\\frac{\\\\partial u}{\\\\partial t} dy = \\\\frac{\\\\partial}{\\\\partial t} \\\\int_{b}^{\\\\eta} udy = \\\\frac{\\\\partial hu}{\\\\partial t}
          \n<\/span><\/span>\u222b<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u222b<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>u<\/span>d<\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>h<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u222bb\u03b7\u2202(u2)\u2202xdy=\u2202\u2202x\u222bb\u03b7u2dy=\u2202(hu2)\u2202x
          \n\\\\int_{b}^{\\\\eta} \\\\frac{\\\\partial (u^2)}{\\\\partial x} dy = \\\\frac{\\\\partial}{\\\\partial x}\\\\int_{b}^{\\\\eta} u^2dy = \\\\frac{\\\\partial (hu^2)}{\\\\partial x}
          \n<\/span><\/span>\u222b<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>u<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u222b<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>u<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>u<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u222bb\u03b7\u2202(uw)\u2202zdy=\u2202\u2202z\u222bb\u03b7uwdy=\u2202(huw)\u2202z
          \n\\\\int_{b}^{\\\\eta} \\\\frac{\\\\partial (uw)}{\\\\partial z} dy = \\\\frac{\\\\partial}{\\\\partial z}\\\\int_{b}^{\\\\eta} uwdy = \\\\frac{\\\\partial (huw)}{\\\\partial z}
          \n<\/span><\/span>\u222b<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>u<\/span>w<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u222b<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>u<\/span>w<\/span>d<\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>u<\/span>w<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u5c06 w \u6539\u4e3a v，\u8868\u793a z \u65b9\u5411\u4e0a\u7684\u6c34\u6d41\u901f\u5ea6\u3002<\/p>\n

          2.4.3 \u5904\u7406\u538b\u5f3a\u68af\u5ea6\u9879<\/h6>\n

          \u6839\u636e\u200b\u9759\u6c34\u538b\u5f3a\u5047\u8bbe\u200b，\u4efb\u610f\u6df1\u5ea6 yy \u5904\u7684\u538b\u5f3a\u7531\u4e0a\u65b9\u6c34\u67f1\u7684\u91cd\u91cf\u4ea7\u751f：<\/p>\n

          p(y)=\u03c1g(\u03b7\u2212y)
          \np(y) = \u03c1g(\u03b7\u2212y)
          \n<\/span><\/span>p<\/span>(<\/span>y<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03c1<\/span>g<\/span>(<\/span>\u03b7<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>y<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          (\u5176\u4e2d \u200b\u03b7 \u200b\u662f\u6c34\u9762\u9ad8\u5ea6，\u03c1 \u200b\u662f\u5bc6\u5ea6，g \u200b\u662f\u91cd\u529b\u52a0\u901f\u5ea6)<\/p>\n

          \u5c06\u5176\u4ee3\u5165\u79ef\u5206（\u5229\u7528\u83b1\u5e03\u5c3c\u8328\u79ef\u5206\u6cd5\u5219，\u5e76\u8003\u8651\u5230\u6c34\u9762 \u03b7\u03b7 \u548c\u6c34\u5e95 bb \u968f xx \u7684\u53d8\u5316）：<\/p>\n

          \u22121\u03c1\u222bb\u03b7\u2202p\u2202xdy=\u2212g\u222bb\u03b7\u2202(\u03b7\u2212y)\u2202xdy=\u2212gh\u2202\u03b7\u2202x
          \n-\\\\frac{1}{\\\\rho}\\\\int_{b}^{\\\\eta} \\\\frac{\\\\partial p}{\\\\partial x}dy = – g\\\\int_{b}^{\\\\eta} \\\\frac{\\\\partial (\\\\eta – y)}{\\\\partial x}dy = – gh\\\\frac{\\\\partial \\\\eta}{\\\\partial x}
          \n<\/span><\/span>\u2212<\/span><\/span><\/span>\u03c1<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u222b<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span><\/span>\u222b<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>\u03b7<\/span><\/span>\u2212<\/span><\/span>y<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span>h<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          2.4.4 \u5904\u7406\u5e95\u5761\/\u5916\u529b\u9879<\/h6>\n

          \u65b9\u7a0b\u53f3\u8fb9\u8fd8\u6709\u4e00\u4e2a\u91cd\u529b\u5728\u5e95\u5761\u4e0a\u7684\u5206\u91cf fx，\u91cd\u529b\u6cbf\u5761\u9762\u7684\u5206\u529b\u4e3a：<\/p>\n

          fx=\u2212g\u2202b\u2202x
          \nf\\\\mathrm{x} = -g\\\\frac{\\\\partial b}{\\\\partial x}
          \n<\/span><\/span>f<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u79ef\u5206\u540e（\u8003\u8651\u5230 hh \u7684\u539a\u5ea6）：<\/p>\n

          \u222bb\u03b7fxdy=\u2212gh\u2202b\u2202x
          \n\\\\int_{b}^{\\\\eta} f\\\\mathrm{x} dy = -gh\\\\frac{\\\\partial b}{\\\\partial x}
          \n<\/span><\/span>\u222b<\/span><\/span>b<\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>f<\/span>x<\/span>d<\/span>y<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span>h<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          2.4.5 \u5408\u5e76\u4e0e\u5316\u7b80<\/h6>\n

          \u6700\u7ec8\u5f97\u5230：<\/p>\n

          \u2202(hu)\u2202t+\u2202\u2202x(hu2+12gh2)+\u2202(huv)\u2202z=\u2212gh\u2202b\u2202x
          \n\\\\frac{\\\\partial (hu)}{\\\\partial t} + \\\\frac{\\\\partial}{\\\\partial x}(hu^2 + \\\\frac{1}{2}gh^2) + \\\\frac{\\\\partial (huv)}{\\\\partial z} = -gh\\\\frac{\\\\partial b}{\\\\partial x}
          \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>u<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>h<\/span>u<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>g<\/span>h<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>uv<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span>h<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u5982\u4e0a\u6211\u4eec\u5c31\u5f97\u5230\u4e86\u5305\u542b\u56fa\u5b9a\u5e95\u5e8a\u8d77\u4f0f\u7684\u4e8c\u7ef4\u975e\u7ebf\u6027 SWE \u65b9\u7a0b\u7ec4：<\/p>\n

          \u2460\u2202h\u2202t+\u2202(hu)\u2202x+\u2202(hv)\u2202z=0
          \n\u2460\\\\frac{\\\\partial h}{\\\\partial t} + \\\\frac{\\\\partial(hu)}{\\\\partial x} + \\\\frac{\\\\partial(hv)}{\\\\partial z} = 0
          \n<\/span><\/span>\u2460<\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>h<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>u<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>v<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u2461\u2202(hu)\u2202t+\u2202\u2202x(hu2+12gh2)+\u2202(huv)\u2202z=\u2212gh\u2202b\u2202x
          \n\u2461\\\\frac{\\\\partial (hu)}{\\\\partial t} + \\\\frac{\\\\partial}{\\\\partial x}(hu^2 + \\\\frac{1}{2}gh^2) + \\\\frac{\\\\partial (huv)}{\\\\partial z} = -gh\\\\frac{\\\\partial b}{\\\\partial x}
          \n<\/span><\/span>\u2461<\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>u<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>h<\/span>u<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>g<\/span>h<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>uv<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span>h<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u2462\u2202(hv)\u2202t+\u2202(huv)\u2202x+\u2202\u2202z(hu2+12gh2)=\u2212gh\u2202b\u2202z
          \n\u2462\\\\frac{\\\\partial (hv)}{\\\\partial t} + \\\\frac{\\\\partial (huv)}{\\\\partial x} + \\\\frac{\\\\partial}{\\\\partial z}(hu^2 + \\\\frac{1}{2}gh^2) = -gh\\\\frac{\\\\partial b}{\\\\partial z}
          \n<\/span><\/span>\u2462<\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>v<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>uv<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>h<\/span>u<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>g<\/span>h<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span>h<\/span><\/span><\/span>\u2202<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          3\u3001\u521d\u59cb\u5316\u9879<\/h4>\n

          \u6709\u5730\u5f62\u65f6，\u4e00\u4e2a\u5173\u952e\u6027\u8d28\u662f：\u6c34\u6df1\u4e0d\u540c，\u4e5f\u53ef\u4ee5\u5b8c\u5168\u9759\u6b62\u3002
          \n\u9759\u6c34\u5e73\u8861\u6ee1\u8db3：<\/p>\n

          u=v=0,\u03b7=\u5e38\u6570
          \nu = v = 0, \\\\eta = \u5e38\u6570
          \n<\/span><\/span>u<\/span><\/span>=<\/span><\/span><\/span><\/span>v<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>\u03b7<\/span><\/span>=<\/span><\/span><\/span><\/span>\u5e38\u6570<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u7531\u4e8e：<\/p>\n

          h=\u03b7\u2212b
          \nh = \\\\eta – b
          \n<\/span><\/span>h<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03b7<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>b<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u5e95\u5e8a\u8d77\u4f0f\u4f1a\u4f7f\u6c34\u6df1\u53d8\u5316，\u4f46\u6c34\u5e73\u6c34\u9762\u4e0d\u4f1a\u56e0\u6b64\u4ea7\u751f\u6c34\u5e73\u52a0\u901f\u5ea6\u3002<\/p>\n

          \u5728\u5b88\u6052\u65b9\u7a0b\u4e2d，\u8fd9\u79cd\u9759\u6b62\u4f9d\u9760\u4e24\u90e8\u5206\u76f8\u4e92\u62b5\u6d88：<\/p>\n

          \u2202\u2202x(12gh2)=\u2212gh\u2202b\u2202x
          \n\\\\frac{\\\\partial}{\\\\partial x} \\\\left(\\\\frac12gh^2\\\\right) = -gh\\\\frac{\\\\partial b}{\\\\partial x}
          \n<\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>g<\/span>h<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span>h<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>b<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u5982\u679c\u7a0b\u5e8f\u5206\u522b\u8fd1\u4f3c\u538b\u529b\u901a\u91cf\u548c\u5e95\u5e8a\u6e90\u9879，\u5374\u6ca1\u6709\u8ba9\u5b83\u4eec\u6b63\u786e\u5e73\u8861，\u5c31\u53ef\u80fd\u51fa\u73b0\u201c\u6ca1\u6709\u65bd\u52a0\u6270\u52a8，\u6c34\u4e5f\u81ea\u5df1\u6d41\u52a8\u201d\u7684\u5047\u8c61\u3002<\/p>\n

          \u80fd\u591f\u5728\u79bb\u6563\u8ba1\u7b97\u4e2d\u4fdd\u6301\u8fd9\u7c7b\u5e73\u8861\u7684\u6570\u503c\u65b9\u6cd5\u79f0\u4e3a \u200bwell-balanced，\u826f\u5e73\u8861\u65b9\u6cd5\u200b\u3002\u9759\u6c34\u91cd\u6784\u662f\u5b9e\u73b0\u8fd9\u4e00\u6027\u8d28\u7684\u4e00\u7c7b\u7ecf\u5178\u65b9\u6cd5\u3002<\/p>\n

          \u56e0\u6b64，\u505a Unity \u5730\u5f62\u6c34\u4f53\u65f6，\u9759\u6c34\u521d\u59cb\u5316\u901a\u5e38\u5e94\u5f53\u662f：<\/p>\n

          h(x,z,0)=max\u2061(\u03b7_0\u2212b(x,z),0)
          \nh(x,z,0)=\\\\max\\\\big(\\\\eta\\\\_0-b(x,z),0\\\\big)
          \n<\/span><\/span>h<\/span>(<\/span>x<\/span>,<\/span><\/span>z<\/span>,<\/span><\/span>0<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>max<\/span><\/span>(<\/span><\/span>\u03b7<\/span>_0<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>b<\/span>(<\/span>x<\/span>,<\/span><\/span>z<\/span>)<\/span>,<\/span><\/span>0<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          4\u3001SWE \u6ce2\u901f<\/h4>\n

          4.1 \u8fde\u7eed\u6027\u65b9\u7a0b<\/h5>\n

          \u8003\u8651\u5e73\u5e95\u3001\u9759\u6b62\u80cc\u666f\u6c34\u4f53，\u5e73\u5747\u6c34\u6df1\u4e3a\u5e38\u6570 H\u3002\u4ee4：<\/p>\n

          h=H+\u03b6
          \nh = H + \\\\zeta
          \n<\/span><\/span>h<\/span><\/span>=<\/span><\/span><\/span><\/span>H<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b6<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u4e3a\u4e86\u63a8\u5bfc\u65b9\u4fbf，\u6211\u4eec\u73b0\u5728\u53ea\u770b\u4e00\u7ef4（x \u65b9\u5411），\u5ffd\u7565 z \u65b9\u5411\u7684\u6d41\u52a8（\u6216\u8005\u5047\u8bbe\u6d41\u52a8\u5728 z \u65b9\u5411\u5747\u5300），\u65b9\u7a0b\u53d8\u6210：<\/p>\n

          \u2202h\u2202t+\u2202(hu)\u2202x=0
          \n\\\\frac{\\\\partial h}{\\\\partial t} + \\\\frac{\\\\partial (hu)}{\\\\partial x} = 0
          \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>h<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>u<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u5229\u7528\u4e58\u79ef\u6c42\u5bfc\u6cd5\u5219\u5c55\u5f00\u7b2c\u4e8c\u9879：<\/p>\n

          \u2202h\u2202t+h\u2202u\u2202x+u\u2202h\u2202x=0
          \n\\\\frac{\\\\partial h}{\\\\partial t} + h\\\\frac{\\\\partial u}{\\\\partial x} + u \\\\frac{\\\\partial h}{\\\\partial x}= 0
          \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>h<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>h<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>u<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>h<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u5f15\u5165\u201c\u5fae\u5c0f\u6270\u52a8（\u5c0f\u632f\u5e45\u6ce2）\u201d\u5047\u8bbe，\u5047\u8bbe\u6c34\u9762\u672c\u6765\u5e73\u9759（\u9759\u6b62\u6c34\u6df1\u4e3a H），\u4f60\u5f80\u6c34\u91cc\u4e22\u4e86\u4e00\u9897\u5c0f\u77f3\u5b50\u3002\u6c34\u9762\u4ea7\u751f\u4e86\u4e00\u4e2a\u975e\u5e38\u5fae\u5c0f\u7684\u6ce2\u6f9c（\u9ad8\u5ea6\u4e3a \u03b6）\u3002<\/p>\n

          \u6b64\u65f6：\u603b\u6c34\u6df1 h(x,t)=H+\u03b6(x,t)，\u5e76\u4e14\u6c34\u6d41\u901f\u5ea6 u(x,t) \u4e5f\u975e\u5e38\u5c0f\u3002<\/p>\n

          \u628a h=H+\u03b6 \u4ee3\u5165\u521a\u624d\u7684\u4e00\u7ef4\u65b9\u7a0b：<\/p>\n

          \u2202(H+\u03b6)\u2202t+(H+\u03b6)\u2202u\u2202x+u\u2202(H+\u03b6)\u2202x=0
          \n\\\\frac{\\\\partial (H+\\\\zeta)}{\\\\partial t} + (H + \\\\zeta)\\\\frac{\\\\partial u}{\\\\partial x} + u\\\\frac{\\\\partial (H+\\\\zeta)}{\\\\partial x} = 0
          \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>H<\/span><\/span>+<\/span><\/span>\u03b6<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>(<\/span>H<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b6<\/span>)<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>u<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>H<\/span><\/span>+<\/span><\/span>\u03b6<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u7531\u4e8eH \u662f\u4e0d\u968f\u65f6\u95f4\u53d8\u5316\u7684\u5e38\u6570，\u5219\u6709：<\/p>\n

          \u2202H\u2202t=\u2202H\u2202x=0
          \n\\\\frac{\\\\partial H}{\\\\partial t} = \\\\frac{\\\\partial H}{\\\\partial x} = 0
          \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>H<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>H<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u53c8\u56e0\u4e3a \u03b6 \u548c u \u90fd\u662f\u5fae\u5c0f\u91cf，\u53ef\u4ee5\u5ffd\u7565，\u4e5f\u6709：<\/p>\n

          \u03b6\u22480,u\u22480
          \n\\\\zeta \\\\approx 0, u \\\\approx 0
          \n<\/span><\/span>\u03b6<\/span><\/span>\u2248<\/span><\/span><\/span><\/span>0<\/span>,<\/span><\/span>u<\/span><\/span>\u2248<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u6240\u4ee5\u539f\u5f0f\u7b49\u4e8e：<\/p>\n

          \u2202\u03b6\u2202t+H\u2202u\u2202x=0
          \n\\\\frac{\\\\partial \\\\zeta}{\\\\partial t} + H\\\\frac{\\\\partial u}{\\\\partial x} = 0
          \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b6<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>H<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          4.2 \u52a8\u91cf\u65b9\u7a0b<\/h5>\n

          \u5728\u53ea\u8003\u8651\u4e00\u7ef4（x\u65b9\u5411）\u4e14\u5ffd\u7565\u5e95\u90e8\u6469\u64e6\u7684\u60c5\u51b5\u4e0b，\u6d45\u6c34\u65b9\u7a0b\u7684\u6807\u51c6\u52a8\u91cf\u65b9\u7a0b\u662f：<\/p>\n

          \u2202u\u2202t+u\u2202u\u2202x=\u2212g\u2202\u03b7\u2202x
          \n\\\\frac{\\\\partial u}{\\\\partial t} + u\\\\frac{\\\\partial u}{\\\\partial x} = -g\\\\frac{\\\\partial \\\\eta}{\\\\partial x}
          \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>u<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

            \n
          • \u200b\u5de6\u8fb9\u200b：\u901f\u5ea6\u968f\u65f6\u95f4\u7684\u53d8\u5316\u7387 + \u200b\u5bf9\u6d41\u52a0\u901f\u5ea6\u200b（\u4f60\u4e4b\u524d\u95ee\u8fc7\u7684，\u6d41\u4f53\u8dd1\u5230\u4e86\u6d41\u901f\u4e0d\u540c\u7684\u5730\u65b9\u4ea7\u751f\u7684\u52a0\u901f\u5ea6）\u3002<\/li>\n
          • \u200b\u53f3\u8fb9\u200b：\u7531\u6c34\u9762\u9ad8\u5ea6\u5dee（\u538b\u529b\u68af\u5ea6）\u4ea7\u751f\u7684\u52a0\u901f\u5ea6（\u6c34\u5f80\u4f4e\u5904\u6d41）\u3002<\/li>\n<\/ul>\n

            \u73b0\u5728，\u5047\u8bbe\u6c34\u9762\u975e\u5e38\u5e73\u9759，\u8f7b\u8f7b\u5439\u4e86\u4e00\u53e3\u6c14，\u4ea7\u751f\u4e86\u4e00\u4e2a\u6781\u5c0f\u7684\u6d9f\u6f2a\u3002<\/p>\n

              \n
            • \u6c34\u6d41\u901f\u5ea6 u \u975e\u5e38\u975e\u5e38\u5c0f（\u8d8b\u8fd1\u4e8e 0）\u3002<\/li>\n
            • \u6c34\u9762\u9ad8\u5ea6\u7684\u53d8\u5316\u91cf \u03b6 \u4e5f\u975e\u5e38\u975e\u5e38\u5c0f\u3002<\/li>\n<\/ul>\n

              \u5219\u6709：<\/p>\n

              u\u2202u\u2202x\u22480
              \nu\\\\frac{\\\\partial u}{\\\\partial x} \\\\approx 0
              \n<\/span><\/span>u<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              \u90a3\u4e48\u539f\u5f0f\u5c31\u53d8\u4e3a：<\/p>\n

              \u2202u\u2202t+g\u2202\u03b7\u2202x=0
              \n\\\\frac{\\\\partial u}{\\\\partial t} + g\\\\frac{\\\\partial \\\\eta}{\\\\partial x} = 0
              \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>g<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              4.3 \u8ba1\u7b97\u6ce2\u901f<\/h5>\n

              \u5bf9\u8fde\u7eed\u6027\u65b9\u7a0b\u4e24\u8fb9\u6c42 t \u7684\u504f\u5bfc：<\/p>\n

              \u22022\u03b6\u2202t2+H\u22022u\u2202x\u2202t=0
              \n\\\\frac{\\\\partial^2 \\\\zeta}{\\\\partial t^2} + H\\\\frac{\\\\partial^2 u}{\\\\partial x \\\\partial t} = 0
              \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b6<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>H<\/span><\/span><\/span>\u2202<\/span>x<\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              \u5bf9\u52a8\u91cf\u65b9\u7a0b\u4e24\u8fb9\u6c42 x \u7684\u504f\u5bfc：<\/p>\n

              \u22022u\u2202x\u2202t+g\u2202\u03b7\u22022x=0
              \n\\\\frac{\\\\partial^2 u}{\\\\partial x \\\\partial t} + g\\\\frac{\\\\partial \\\\eta}{\\\\partial^2 x} = 0
              \n<\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>g<\/span><\/span><\/span>\u2202<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              \u8054\u7acb\u5f97\u5230：<\/p>\n

              \u22022\u03b6\u2202t2=Hg\u22022\u03b7\u2202x2
              \n\\\\frac{\\\\partial^2 \\\\zeta}{\\\\partial t^2} = Hg\\\\frac{\\\\partial^2 \\\\eta}{\\\\partial x^2}
              \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b6<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>H<\/span>g<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              \u53c8\u56e0\u4e3a：<\/p>\n

              \u03b7=\u03b6+H
              \n\\\\eta = \\\\zeta + H
              \n<\/span><\/span>\u03b7<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03b6<\/span><\/span>+<\/span><\/span><\/span><\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              \u5219\u6709：<\/p>\n

              \u22022\u03b7\u2202t2=Hg\u22022\u03b7\u2202x2
              \n\\\\frac{\\\\partial^2 \\\\eta}{\\\\partial t^2} = Hg\\\\frac{\\\\partial^2 \\\\eta}{\\\\partial x^2}
              \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>H<\/span>g<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              \u6ce2\u52a8\u65b9\u7a0b\u6807\u51c6\u5f62\u5f0f\u4e3a：<\/p>\n

              \u22022\u03b7\u2202t2=c2\u22022\u03b7\u2202x2
              \n\\\\frac{\\\\partial^2 \\\\eta}{\\\\partial t^2} = c^2\\\\frac{\\\\partial^2 \\\\eta}{\\\\partial x^2}
              \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>c<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              \u6240\u4ee5\u5f97\u5230\u7269\u7406\u6ce2\u901f\u516c\u5f0f：<\/p>\n

              c=gH
              \nc = \\\\sqrt{gH}
              \n<\/span><\/span>c<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>g<\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \n
              • g \u662f\u91cd\u529b\u52a0\u901f\u5ea6（\u7ea6 9.81\u2009m\/s29.81m\/s2）<\/li>\n
              • HH \u662f\u200b\u9759\u6c34\u6df1\u200b（\u6216\u8005\u5f53\u5730\u5b9e\u9645\u6c34\u6df1 hh）<\/li>\n<\/ul>\n

                \u200b\u8fd9\u4e2a\u516c\u5f0f\u975e\u5e38\u76f4\u89c2\u200b：<\/p>\n

                  \n
                • \u6c34\u8d8a\u6df1，\u6ce2\u4f20\u5f97\u8d8a\u5feb（\u592a\u5e73\u6d0b\u91cc\u7684\u6d77\u5578\u901f\u5ea6\u63a5\u8fd1\u98de\u673a）\u3002<\/li>\n
                • \u6c34\u8d8a\u6d45，\u6ce2\u4f20\u5f97\u8d8a\u6162（\u51b2\u4e0a\u6d77\u6ee9\u7684\u6ce2\u6d6a\u4f1a\u51cf\u901f）\u3002<\/li>\n<\/ul>\n

                  \u4e09\u3001\u6570\u503c\u79bb\u6563\u65b9\u6cd5<\/h3>\n

                  \u4ece\u65b9\u7a0b\u5230\u7a0b\u5e8f，\u9700\u8981\u9009\u62e9\u6570\u503c\u79bb\u6563\u65b9\u6cd5\u3002SWE \u672c\u8eab\u5e76\u4e0d\u662f\u67d0\u4e00\u79cd\u56fa\u5b9a\u7b97\u6cd5\u3002<\/p>\n

                  \u5e38\u89c1\u7684\u5c42\u6b21\u5173\u7cfb\u662f：<\/p>\n\n\u5c42\u6b21\u89e3\u51b3\u7684\u95ee\u9898\u793a\u4f8b<\/tr>\n\n\n\n\n\n
                  \u7269\u7406\u6a21\u578b<\/td>\n\u6c34\u9075\u5faa\u4ec0\u4e48\u89c4\u5f8b<\/td>\n\u975e\u7ebf\u6027 SWE\u3001\u7ebf\u6027 SWE<\/td>\n<\/tr>\n
                  \u7a7a\u95f4\u79bb\u6563<\/td>\n\u600e\u6837\u8868\u793a\u7a7a\u95f4\u53d8\u5316<\/td>\n\u6709\u9650\u5dee\u5206\u3001\u6709\u9650\u4f53\u79ef\u3001\u6709\u9650\u5143<\/td>\n<\/tr>\n
                  \u754c\u9762\u901a\u91cf<\/td>\n\u76f8\u90bb\u5355\u5143\u4e4b\u95f4\u4ea4\u6362\u591a\u5c11\u91cf<\/td>\nRusanov\u3001HLL\u3001Roe<\/td>\n<\/tr>\n
                  \u65f6\u95f4\u63a8\u8fdb<\/td>\n\u600e\u6837\u4ece\u5f53\u524d\u72b6\u6001\u63a8\u8fdb\u5230\u4e0b\u4e00\u65f6\u523b<\/td>\n\u663e\u5f0f Euler\u3001Runge\u2013Kutta<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                  3.1 \u7269\u7406\u6a21\u578b<\/h4>\n

                  3.1.1 \u9009\u62e9\u7269\u7406\u6a21\u578b\u7684\u76ee\u7684<\/h5>\n

                  \u771f\u5b9e\u6c34\u4f53\u5305\u542b\u5927\u91cf\u73b0\u8c61：<\/p>\n

                    \n
                  • \u6c34\u5e73\u6d41\u52a8\u3001\u7ad6\u76f4\u8fd0\u52a8；<\/li>\n
                  • \u538b\u529b\u53d8\u5316；<\/li>\n
                  • \u9ecf\u6027\u3001\u6469\u64e6\u548c\u6e4d\u6d41；<\/li>\n
                  • \u6ce2\u6d6a\u4f20\u64ad\u3001\u7834\u788e\u3001\u98de\u6e85；<\/li>\n
                  • \u4e0d\u540c\u6ce2\u957f\u7684\u6ce2\u4ee5\u4e0d\u540c\u901f\u5ea6\u4f20\u64ad\u3002<\/li>\n<\/ul>\n

                    \u5982\u679c\u5b8c\u6574\u4fdd\u7559\u8fd9\u4e9b\u73b0\u8c61，\u6c42\u89e3\u6210\u672c\u4f1a\u975e\u5e38\u9ad8\u3002\u56e0\u6b64，\u9700\u8981\u9009\u62e9\u4e00\u4e2a\u9002\u5408\u7814\u7a76\u76ee\u6807\u7684\u7b80\u5316\u6a21\u578b\u3002<\/p>\n

                    SWE \u7684\u4e3b\u8981\u7b80\u5316\u662f：\u6cbf\u6c34\u6df1\u65b9\u5411\u8fdb\u884c\u5e73\u5747，\u7528\u6c34\u6df1\u548c\u6df1\u5ea6\u5e73\u5747\u6c34\u5e73\u901f\u5ea6\u63cf\u8ff0\u6c34\u4f53，\u5e76\u91c7\u7528\u9759\u6c34\u538b\u529b\u8fd1\u4f3c\u3002\u5b83\u9002\u7528\u4e8e\u6c34\u6df1\u76f8\u5bf9\u6c34\u5e73\u8fd0\u52a8\u5c3a\u5ea6\u8f83\u5c0f\u7684\u60c5\u51b5\u3002<\/p>\n

                    \u9009\u62e9\u7269\u7406\u6a21\u578b，\u672c\u8d28\u4e0a\u662f\u5728\u51b3\u5b9a：\u54ea\u4e9b\u73b0\u8c61\u9700\u8981\u8ba1\u7b97，\u54ea\u4e9b\u73b0\u8c61\u53ef\u4ee5\u8fd1\u4f3c\u6216\u5ffd\u7565\u3002<\/p>\n

                    3.1.2 \u4e00\u7ef4\u975e\u7ebf\u6027 SWE<\/h5>\n

                    \u5bf9\u4e8e\u5e73\u5e95\u3001\u6ca1\u6709\u6469\u64e6\u548c\u5916\u529b\u7684\u4e00\u7ef4\u6c34\u6d41，\u975e\u7ebf\u6027 SWE \u4e3a：<\/p>\n

                    \u2202h\u2202t+\u2202(hu)\u2202x=0
                    \n\\\\frac{\\\\partial h}{\\\\partial t} + \\\\frac{\\\\partial (hu)}{\\\\partial x} = 0
                    \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>h<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>u<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                    \u2202(hu)\u2202x+\u2202\u2202x(hu2+12gh2)=0
                    \n\\\\frac{\\\\partial (hu)}{\\\\partial x} + \\\\frac{\\\\partial }{\\\\partial x}(hu^2 + \\\\frac{1}{2}gh^2) = 0
                    \n<\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>(<\/span>h<\/span>u<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>h<\/span>u<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>g<\/span>h<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                    \u7b2c\u4e00\u6761\u63cf\u8ff0\u8d28\u91cf\u5b88\u6052，\u7b2c\u4e8c\u6761\u63cf\u8ff0\u6c34\u5e73\u52a8\u91cf\u5b88\u6052\u3002<\/p>\n

                    \u5b9a\u4e49\u72b6\u6001\u5411\u91cf：<\/p>\n

                    U=[hm],m=hu
                    \nU = \\\\begin{bmatrix} h \\\\\\\\ m \\\\end{bmatrix}, m = hu
                    \n<\/span><\/span>U<\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>h<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span>,<\/span><\/span>m<\/span><\/span>=<\/span><\/span><\/span><\/span>h<\/span>u<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                    \u5176\u4e2d，m \u662f\u7701\u7565\u5e38\u6570\u5bc6\u5ea6\u56e0\u5b50\u7684\u52a8\u91cf\u53d8\u91cf\u3002<\/p>\n

                    \u518d\u5b9a\u4e49\u7269\u7406\u901a\u91cf：<\/p>\n

                    F(U)=[mm2h+12gh2]
                    \nF(U) = \\\\begin{bmatrix} m \\\\\\\\ \\\\frac{m^2}{h} + \\\\frac{1}{2}gh^2 \\\\end{bmatrix}
                    \n<\/span><\/span>F<\/span>(<\/span>U<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/span>h<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>m<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>g<\/span>h<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                    \u4e8e\u662f，\u4e24\u6761\u65b9\u7a0b\u53ef\u4ee5\u7edf\u4e00\u5199\u6210：<\/p>\n

                    \u2202U\u2202t+\u2202F(U)\u2202x=0
                    \n\\\\frac{\\\\partial U}{\\\\partial t} + \\\\frac{\\\\partial F(U)}{\\\\partial x} = 0
                    \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>U<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>F<\/span>(<\/span>U<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                    \u8fd9\u91cc\u7684\u201c\u975e\u7ebf\u6027\u201d，\u610f\u5473\u7740\u72b6\u6001\u91cf\u4e4b\u95f4\u5b58\u5728\u4e58\u79ef\u3001\u5e73\u65b9\u7b49\u5173\u7cfb\u3002\u4f8b\u5982：<\/p>\n

                    hu，hu2，h2
                    \nhu，hu^2，h^2
                    \n<\/span><\/span>h<\/span>u<\/span>，<\/span>h<\/span>u<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，<\/span>h<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                    \u6c34\u6df1\u548c\u901f\u5ea6\u4f1a\u76f8\u4e92\u5f71\u54cd，\u6ce2\u7684\u4f20\u64ad\u901f\u5ea6\u4e5f\u4f9d\u8d56\u5f53\u524d\u72b6\u6001：<\/p>\n

                    u\u2212gh，u+gh
                    \nu – \\\\sqrt{gh}，u+\\\\sqrt{gh}
                    \n<\/span><\/span>u<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>g<\/span>h<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>，<\/span>u<\/span><\/span>+<\/span><\/span><\/span><\/span><\/span>g<\/span>h<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                    \u56e0\u6b64，\u6ce2\u6d6a\u7684\u4e0d\u540c\u90e8\u5206\u53ef\u80fd\u5177\u6709\u4e0d\u540c\u4f20\u64ad\u901f\u5ea6，\u9010\u6e10\u5f62\u6210\u9661\u5ced\u6ce2\u9762，\u751a\u81f3\u51fa\u73b0\u6c34\u8dc3\u7b49\u95f4\u65ad\u7ed3\u6784\u3002<\/p>\n

                    3.1.3 \u4e00\u7ef4\u7ebf\u6027 SWEH<\/h5>\n

                    \u5047\u8bbe\u6c34\u4f53\u6700\u521d\u9759\u6b62，\u5e73\u5747\u6c34\u6df1\u4e3a\u5e38\u6570 H，\u6270\u52a8\u4e3a \u03b6：<\/p>\n

                    h=H+\u03b6
                    \nh = H + \\\\zeta
                    \n<\/span><\/span>h<\/span><\/span>=<\/span><\/span><\/span><\/span>H<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b6<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                    \u7ebf\u6027\u5316\u65f6\u5ffd\u7565\u6270\u52a8\u91cf\u4e4b\u95f4\u7684\u9ad8\u9636\u4e58\u79ef，\u5316\u7b80\u8fde\u7eed\u6027\u65b9\u7a0b\u5f97\u5230：<\/p>\n

                    \u2202\u03b6\u2202t+H\u2202u\u2202x=0
                    \n\\\\frac{\\\\partial \\\\zeta}{\\\\partial t} + H\\\\frac{\\\\partial u}{\\\\partial x} = 0
                    \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b6<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>H<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                    \u52a8\u91cf\u65b9\u7a0b\u76f8\u5e94\u7b80\u5316\u4e3a：<\/p>\n

                    \u2202u\u2202t+g\u2202\u03b6\u2202x=0
                    \n\\\\frac{\\\\partial u}{\\\\partial t} + g\\\\frac{\\\\partial \\\\zeta}{\\\\partial x} = 0
                    \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>g<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b6<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                    \u5b83\u4eec\u63cf\u8ff0\u56f4\u7ed5\u9759\u6b62\u80cc\u666f\u7684\u5c0f\u6270\u52a8\u4f20\u64ad，\u6ce2\u901f\u4e3a：<\/p>\n

                    c=gH
                    \nc = \\\\sqrt{gH}
                    \n<\/span><\/span>c<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>g<\/span>H<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                    3.1.4 \u4e24\u79cd\u7269\u7406\u6a21\u578b\u7684\u533a\u522b<\/h5>\n\n\u6bd4\u8f83\u5185\u5bb9\u7ebf\u6027 SWE\u975e\u7ebf\u6027 SWE<\/tr>\n\n\n\n\n\n\n
                    \u4e3b\u8981\u63cf\u8ff0\u5bf9\u8c61<\/td>\n\u80cc\u666f\u72b6\u6001\u9644\u8fd1\u7684\u5c0f\u6270\u52a8<\/td>\n\u8f83\u4e00\u822c\u7684\u6d45\u6c34\u6d41\u52a8<\/td>\n<\/tr>\n
                    \u72b6\u6001\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528<\/td>\n\u7ecf\u8fc7\u7ebf\u6027\u5316\u7b80\u5316<\/td>\n\u4fdd\u7559\u975e\u7ebf\u6027\u8026\u5408<\/td>\n<\/tr>\n
                    \u9759\u6b62\u3001\u5e38\u6c34\u6df1\u80cc\u666f\u7684\u6ce2\u901f<\/td>\n\u56fa\u5b9a\u4e3a\\\\(\\\\sqrt{gH}\\\\)<\/td>\n\u968f\u5c40\u90e8\u6c34\u6df1\u3001\u6d41\u901f\u53d8\u5316<\/td>\n<\/tr>\n
                    \u6c34\u8dc3\u3001\u660e\u663e\u7684\u6ce2\u9762\u9661\u5316<\/td>\n\u4e0d\u80fd\u5b8c\u6574\u63cf\u8ff0<\/td>\n\u53ef\u4ee5\u63cf\u8ff0，\u9700\u5408\u9002\u7684\u6570\u503c\u683c\u5f0f<\/td>\n<\/tr>\n
                    \u5178\u578b\u7528\u9014<\/td>\n\u5c0f\u6ce2\u52a8\u5206\u6790\u3001\u7b80\u5316\u6ce2\u7eb9\u6a21\u62df<\/td>\n\u6d45\u6c34\u6d41\u52a8\u3001\u6e83\u575d\u3001\u4ea4\u4e92\u6c34\u4f53\u7b49<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                    \u628a\u7f51\u683c\u52a0\u5bc6，\u4e0d\u80fd\u8865\u56de\u7269\u7406\u6a21\u578b\u5df2\u7ecf\u5ffd\u7565\u7684\u73b0\u8c61\u3002<\/p>\n

                    \u4f8b\u5982，\u7ebf\u6027 SWE \u5373\u4f7f\u7528\u5f88\u7ec6\u7684\u7f51\u683c，\u4e5f\u4e0d\u4f1a\u81ea\u52a8\u53d8\u6210\u975e\u7ebf\u6027 SWE；\u57fa\u7840 SWE \u5373\u4f7f\u6c42\u89e3\u5f97\u975e\u5e38\u7cbe\u786e，\u4e5f\u4e0d\u4f1a\u81ea\u52a8\u4ea7\u751f\u771f\u5b9e\u6c34\u6ef4\u548c\u7ffb\u5377\u6d6a\u5934\u3002<\/p>\n

                    \u6b64\u5916，\u7269\u7406\u95ee\u9898\u8fd8\u9700\u8981\u914d\u5957\u7684\u521d\u59cb\u6761\u4ef6\u3001\u8fb9\u754c\u6761\u4ef6\u548c\u5916\u90e8\u4f5c\u7528\u3002\u4f8b\u5982：\u6700\u521d\u7684\u6c34\u6df1\u3001\u5899\u58c1\u4f4d\u7f6e\u3001\u5165\u53e3\u6d41\u91cf，\u4ee5\u53ca\u7269\u4f53\u600e\u6837\u5411\u6c34\u4f53\u65bd\u52a0\u6270\u52a8\u3002<\/p>\n

                    3.2 \u7a7a\u95f4\u79bb\u6563<\/h4>\n

                    3.2.1 \u7a7a\u95f4\u79bb\u6563\u7684\u542b\u4e49<\/h5>\n

                    \u8fde\u7eed\u6a21\u578b\u4e2d\u7684：<\/p>\n

                    h(x,t)，u(x,t)
                    \nh(x, t)，u(x, t)
                    \n<\/span><\/span>h<\/span>(<\/span>x<\/span>,<\/span><\/span>t<\/span>)<\/span>，<\/span>u<\/span>(<\/span>x<\/span>,<\/span><\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                    \u5728\u4efb\u610f\u4f4d\u7f6e\u90fd\u5177\u6709\u503c\u3002\u8ba1\u7b97\u673a\u65e0\u6cd5\u4fdd\u5b58\u65e0\u9650\u591a\u4e2a\u4f4d\u7f6e，\u56e0\u6b64\u9700\u8981\u7528\u6709\u9650\u4e2a\u6570\u636e\u8fd1\u4f3c\u6574\u4e2a\u7a7a\u95f4\u3002<\/p>\n

                    \u4f8b\u5982，\u5c06\u4e00\u6761\u6c34\u69fd\u5212\u5206\u4e3a N \u4e2a\u533a\u57df：<\/p>\n

                    \u0394x=LN
                    \n\\\\Delta x = \\\\frac{L}{N}
                    \n<\/span><\/span>\u0394<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>N<\/span><\/span><\/span><\/span><\/span><\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                    \u4f46\u201c\u5212\u5206\u7f51\u683c\u201d\u53ea\u662f\u5f00\u59cb，\u8fd8\u9700\u8981\u660e\u786e：<\/p>\n

                      \n
                    • \u6bcf\u4e2a\u4f4d\u7f6e\u4fdd\u5b58\u4ec0\u4e48；<\/li>\n
                    • \u4e00\u4e2a\u533a\u57df\u5185\u90e8\u7684\u72b6\u6001\u600e\u6837\u8868\u793a；<\/li>\n
                    • \u7a7a\u95f4\u5bfc\u6570\u6216\u533a\u57df\u79ef\u5206\u600e\u6837\u8fd1\u4f3c\u3002<\/li>\n<\/ul>\n

                      \u6709\u9650\u5dee\u5206\u3001\u6709\u9650\u4f53\u79ef\u548c\u6709\u9650\u5143，\u5728\u8fd9\u4e9b\u95ee\u9898\u4e0a\u91c7\u7528\u4e0d\u540c\u601d\u8def\u3002\u4e0b\u9762\u901a\u8fc7\u4e00\u7ef4\u7f51\u683c\u6765\u4ecb\u7ecd\u8fd9\u4e9b\u65b9\u6cd5\u3002<\/p>\n

                      3.2.2 \u6709\u9650\u5dee\u5206\u6cd5<\/h5>\n

                      \u6709\u9650\u5dee\u5206\u6cd5\u901a\u5e38\u4fdd\u5b58\u82e5\u5e72\u4f4d\u7f6e\u4e0a\u7684\u51fd\u6570\u503c：<\/p>\n

                      hi(t)\u2248h(xi,t)
                      \nh_i(t)\\\\approx h(x_i,t)
                      \n<\/span><\/span>h<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>t<\/span>)<\/span><\/span>\u2248<\/span><\/span><\/span><\/span>h<\/span>(<\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>t<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                      \u4f8b\u5982，\u7528\u4e2d\u5fc3\u5dee\u5206\u8fd1\u4f3c\u6c34\u9762\u5761\u5ea6：<\/p>\n

                      \u2202\u03b7\u2202x\u2223xi\u2248\u03b7i+1\u2212\u03b7i\u221212\u0394x
                      \n\\\\left. \\\\frac{\\\\partial \\\\eta}{\\\\partial x} \\\\right |_{x_i} \\\\approx \\\\frac{\\\\eta_{i+1}-\\\\eta_{i-1}}{2\\\\Delta x}
                      \n<\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span><\/span><\/span>2\u0394<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b7<\/span><\/span>i<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>\u03b7<\/span><\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                      \u5982\u679c\u91c7\u7528\u7ebf\u6027 SWE：<\/p>\n

                      \u2202u\u2202t=\u2212g\u2202\u03b6\u2202x
                      \n\\\\frac{\\\\partial u}{\\\\partial t} = -g\\\\frac{\\\\partial \\\\zeta}{\\\\partial x}
                      \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>u<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>\u03b6<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                      \u7a7a\u95f4\u79bb\u6563\u540e\u5c31\u5f97\u5230：<\/p>\n

                      duidt\u2248\u2212g\u03b6i+1\u2212\u03b6i\u221212\u0394x
                      \n\\\\frac{du_i}{dt} \\\\approx -g\\\\frac{\\\\zeta_{i+1}-\\\\zeta_{i-1}}{2\\\\Delta x}
                      \n<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>u<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>\u2212<\/span>g<\/span><\/span><\/span>2\u0394<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b6<\/span><\/span>i<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span>\u03b6<\/span><\/span>i<\/span>\u2212<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                      \u539f\u672c\u8fde\u7eed\u7684\u7a7a\u95f4\u5bfc\u6570，\u53d8\u6210\u4e86\u76f8\u90bb\u6570\u636e\u4e4b\u95f4\u7684\u8fd0\u7b97\u3002\u6ce8\u610f，\u6b64\u65f6\u53ea\u5b8c\u6210\u4e86\u7a7a\u95f4\u79bb\u6563，\u8fd8\u6ca1\u6709\u51b3\u5b9a\u5982\u4f55\u63a8\u8fdb\u65f6\u95f4\u3002<\/p>\n

                      \u6709\u9650\u5dee\u5206\u6cd5\u7684\u76f4\u89c2\u7279\u70b9\u662f：<\/p>\n

                        \n
                      • \u5bf9\u89c4\u5219\u7f51\u683c\u5f88\u5bb9\u6613\u5b9e\u73b0；<\/li>\n
                      • \u76f8\u90bb\u91c7\u6837\u548c\u7eb9\u7406\u64cd\u4f5c\u6bd4\u8f83\u81ea\u7136；<\/li>\n
                      • \u53ef\u4ee5\u6784\u9020\u9ad8\u9636\u5bfc\u6570\u8fd1\u4f3c；<\/li>\n
                      • \u7a33\u5b9a\u6027\u548c\u5b88\u6052\u6027\u53d6\u51b3\u4e8e\u5177\u4f53\u683c\u5f0f\u3002<\/li>\n<\/ul>\n

                        \u7a7a\u95f4\u79bb\u6563（\u7b97\u7a7a\u95f4\u5bfc\u6570）\u548c\u65f6\u95f4\u79bb\u6563（\u7b97\u65f6\u95f4\u63a8\u8fdb）\u5fc5\u987b\u6ee1\u8db3\u7a33\u5b9a\u6027\u6761\u4ef6（CFL \u6761\u4ef6），\u4e14\u4e0d\u540c\u7ec4\u5408\u7684\u7a33\u5b9a\u6027\u5b8c\u5168\u4e0d\u540c\u3002 \u4e0d\u8981\u4ee5\u4e3a\u968f\u4fbf\u7528\u4ec0\u4e48\u65b9\u6cd5（\u6bd4\u5982\u4e2d\u5fc3\u5dee\u5206 + \u663e\u793a\u65f6\u95f4\u63a8\u8fdb）\u90fd\u80fd\u7b97\u51fa\u6b63\u786e\u7ed3\u679c\u3002<\/p>\n

                        3.2.3 \u6709\u9650\u4f53\u79ef\u6cd5<\/h5>\n

                        \u6709\u9650\u4f53\u79ef\u6cd5\u628a\u6bcf\u4e2a\u7f51\u683c\u89c6\u4e3a\u4e00\u4e2a\u6709\u5927\u5c0f\u7684\u63a7\u5236\u4f53\u3002<\/p>\n

                        1\u3001\u6709\u9650\u4f53\u79ef\u6cd5\u533a\u57df\u5185\u5b58\u91cf\u53d8\u5316\u8ba1\u7b97<\/h6>\n

                        \u4e00\u7ef4\u60c5\u51b5\u4e0b，\u5355\u5143 i \u7684\u5de6\u53f3\u8fb9\u754c\u4e3a：<\/p>\n

                        xi\u221212，xi+12
                        \nx_{i – \\\\frac{1}{2}}，x_{i + \\\\frac{1}{2}}
                        \n<\/span><\/span>x<\/span><\/span>i<\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，<\/span>x<\/span><\/span>i<\/span>+<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                        \u8fd9\u91cc：<\/p>\n

                          \n
                        • \u6574\u6570\u4e0b\u6807 i：\u5355\u5143；<\/li>\n
                        • \u534a\u6574\u6570\u4e0b\u6807 i+1\/2：\u4e24\u4e2a\u5355\u5143\u4e4b\u95f4\u7684\u754c\u9762\u3002<\/li>\n<\/ul>\n

                          \u4fdd\u5b58\u7684\u72b6\u6001\u662f\u5355\u5143\u5e73\u5747\u503c：<\/p>\n

                          Ui\u203e=1\u0394x\u222bxi\u221212xi+12U(x,t)\u2009dx
                          \n\\\\overline{U_i} = \\\\frac{1}{\\\\Delta x}\\\\int_{x_{i-\\\\frac{1}{2}}}^{x_{i+\\\\frac{1}{2}}} U(x, t)\\\\,dx
                          \n<\/span><\/span><\/span>U<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u0394<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u222b<\/span><\/span>x<\/span><\/span>i<\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span>+<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>U<\/span>(<\/span>x<\/span>,<\/span><\/span>t<\/span>)<\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u516c\u5f0f\u4e24\u8fb9\u540c\u65f6\u5bf9\u65f6\u95f4 t \u6c42\u5bfc\u6570：<\/p>\n

                          Ui\u203e=ddt(1\u0394x\u222bxi\u221212xi+12U(x,t)\u2009dx)
                          \n\\\\overline{U_i} = \\\\frac{d}{dt} \\\\left ( \\\\frac{1}{\\\\Delta x}\\\\int_{x_{i-\\\\frac{1}{2}}}^{x_{i+\\\\frac{1}{2}}} U(x, t)\\\\,dx \\\\right )
                          \n<\/span><\/span><\/span>U<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u0394<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u222b<\/span><\/span>x<\/span><\/span>i<\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span>+<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>U<\/span>(<\/span>x<\/span>,<\/span><\/span>t<\/span>)<\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u79ef\u5206\u533a\u95f4\u56fa\u5b9a，\u53ef\u4ee5\u7531\u83b1\u5e03\u5c3c\u8328\u79ef\u5206\u6cd5\u5219\u628a\u65f6\u95f4\u5bfc\u6570\u76f4\u63a5\u79fb\u5230\u79ef\u5206\u62ec\u53f7\u91cc\u9762：<\/p>\n

                          Ui\u203e=1\u0394x\u222bxi\u221212xi+12\u2202U(x,t)\u2202t\u2009dx
                          \n\\\\overline{U_i} = \\\\frac{1}{\\\\Delta x}\\\\int_{x_{i-\\\\frac{1}{2}}}^{x_{i+\\\\frac{1}{2}}} \\\\frac{\\\\partial U(x, t)}{\\\\partial t}\\\\,dx
                          \n<\/span><\/span><\/span>U<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u0394<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u222b<\/span><\/span>x<\/span><\/span>i<\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span>+<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>U<\/span>(<\/span>x<\/span>,<\/span><\/span>t<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u7531\u4e00\u7ef4\u6d45\u6c34\u65b9\u7a0b\u6838\u5fc3\u90e8\u5206：<\/p>\n

                          \u2202U\u2202t+\u2202F\u2202x=0
                          \n\\\\frac{\\\\partial U}{\\\\partial t} + \\\\frac{\\\\partial F}{\\\\partial x} = 0
                          \n<\/span><\/span><\/span><\/span>\u2202<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>U<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>F<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u5176\u4e2d\u2009U=[h,hu]T，F=[hu,hu2+12gh2]T
                          \n\u5176\u4e2d\\\\,U=[h, hu]^T，F = [hu, hu^2+\\\\frac{1}{2}gh^2]^T
                          \n<\/span><\/span>\u5176\u4e2d<\/span><\/span>U<\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span>h<\/span>,<\/span><\/span>h<\/span>u<\/span>]<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，<\/span>F<\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span>h<\/span>u<\/span>,<\/span><\/span>h<\/span>u<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>g<\/span>h<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span>T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u5c06\u5176\u5e26\u5165\u521a\u624d\u7684\u79ef\u5206\u4e2d：<\/p>\n

                          dUi\u203edt=1\u0394x\u222bxi\u221212xi+12(\u2212\u2202F(x,t)\u2202x)dx
                          \n\\\\frac{d\\\\overline{U_i}}{dt} = \\\\frac{1}{\\\\Delta x}\\\\int_{x_{i-\\\\frac{1}{2}}}^{x_{i+\\\\frac{1}{2}}} \\\\left ( -\\\\frac{\\\\partial F(x, t)}{\\\\partial x}\\\\right )dx
                          \n<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>U<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>\u0394<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u222b<\/span><\/span>x<\/span><\/span>i<\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span>+<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>\u2212<\/span><\/span><\/span>\u2202<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2202<\/span>F<\/span>(<\/span>x<\/span>,<\/span><\/span>t<\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>d<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u6700\u7ec8\u5f97\u5230：<\/p>\n

                          dUi\u203edt=\u2212F(xi+12)\u2212F(xi\u221212)\u0394x
                          \n\\\\frac{d\\\\overline{U_i}}{dt} = -\\\\frac{F(x_{i+\\\\frac{1}{2}}) – F(x_{i-\\\\frac{1}{2}})}{\\\\Delta x}
                          \n<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>U<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>\u0394<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>F<\/span>(<\/span>x<\/span><\/span>i<\/span>+<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span>F<\/span>(<\/span>x<\/span><\/span>i<\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u5b9e\u9645\u8ba1\u7b97\u65f6，\u518d\u7528\u6570\u503c\u901a\u91cf\u8fd1\u4f3c\u754c\u9762\u901a\u91cf：<\/p>\n

                          dUi\u203edt=\u2212F^(xi+12)\u2212F^(xi\u221212)\u0394x
                          \n\\\\frac{d\\\\overline{U_i}}{dt} = -\\\\frac{\\\\widehat{F}(x_{i+\\\\frac{1}{2}})- \\\\widehat{F}(x_{i-\\\\frac{1}{2}})}{\\\\Delta x}
                          \n<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>U<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>\u0394<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>F<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span><\/span>i<\/span>+<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span>F<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span><\/span>i<\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u4e0a\u5f0f\u8868\u8fbe\u7684\u662f：\u5355\u5143\u5185\u90e8\u5b58\u91cf\u7684\u53d8\u5316\u3002\u7531\u5de6\u53f3\u4e24\u4fa7\u7684\u51c0\u6d41\u5165\u51b3\u5b9a\u3002<\/p>\n

                          2\u3001\u6709\u9650\u4f53\u79ef\u5143\u7684\u5185\u90e8\u5b88\u6052\u53d8\u91cf\u7684\u5904\u7406<\/h6>\n

                          \u2460 \u5e38\u6570<\/p>\n

                          \u6709\u9650\u4f53\u79ef\u6cd5\u5e76\u4e0d\u610f\u5473\u7740\u6bcf\u4e2a\u5355\u5143\u5185\u90e8\u6c38\u8fdc\u53ea\u80fd\u662f\u4e00\u4e2a\u5e38\u6570\u3002\u6700\u7b80\u5355\u7684\u505a\u6cd5\u662f\u5206\u7247\u5e38\u6570，\u5373\u6574\u4e2a\u5355\u5143\u90fd\u4f7f\u7528\u540c\u4e00\u4e2a\u72b6\u6001\u3002\u8fd9\u901a\u5e38\u5bf9\u5e94\u57fa\u7840\u7684\u4e00\u9636\u7a7a\u95f4\u8fd1\u4f3c\u3002\u5373：<\/p>\n

                          U(x)\u2248U\u203ei
                          \nU(x) \\\\approx \\\\overline{U}_i
                          \n<\/span><\/span>U<\/span>(<\/span>x<\/span>)<\/span><\/span>\u2248<\/span><\/span><\/span><\/span><\/span>U<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u2461 \u7ebf\u6027\u91cd\u6784<\/p>\n

                          \u4f7f\u7528\u5206\u7247\u7ebf\u6027\u91cd\u6784：<\/p>\n

                          Ui(x)\u2248U\u203ei+\u03c3i(x\u2212xi)
                          \nU_i(x) \\\\approx \\\\overline{U}_i + \\\\sigma_i(x – x_i)
                          \n<\/span><\/span>U<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span>)<\/span><\/span>\u2248<\/span><\/span><\/span><\/span><\/span>U<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03c3<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u5176\u4e2d \u03c3i \u662f\u5355\u5143\u5185\u7684\u659c\u7387\u3002<\/p>\n

                          \u8fd9\u6837\u53ef\u4ee5\u66f4\u597d\u5730\u8868\u793a\u5e73\u6ed1\u6ce2\u5f62\u3002\u4f46\u5728\u9661\u5ced\u6ce2\u9762\u9644\u8fd1，\u76f4\u63a5\u4f7f\u7528\u8f83\u5927\u7684\u659c\u7387\u53ef\u80fd\u4ea7\u751f\u8fc7\u51b2，\u4f8b\u5982\u8ba1\u7b97\u51fa\u4e0d\u5408\u7406\u7684\u8d1f\u6c34\u6df1\u3002\u56e0\u6b64，\u901a\u5e38\u9700\u8981\u9650\u5236\u5668；\u5bf9\u4e8e SWE，\u8fd8\u53ef\u80fd\u9700\u8981\u989d\u5916\u7684\u6b63\u6c34\u6df1\u7ea6\u675f\u4e0e\u9759\u6c34\u5e73\u8861\u5904\u7406\u3002<\/p>\n

                          3.2.4 \u6709\u9650\u5143\u6cd5<\/h5>\n

                          \u6709\u9650\u5143\u6cd5\u7684\u57fa\u672c\u5f62\u5f0f\u662f：<\/p>\n

                          Uh(x,t)=\u2211jaj(t)\u03d5j(x)
                          \nU_h(x, t) = \\\\sum_{j}a_j(t) \\\\phi_j(x)
                          \n<\/span><\/span>U<\/span><\/span>h<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span>,<\/span><\/span>t<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>j<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>t<\/span>)<\/span>\u03d5<\/span><\/span>j<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>x<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                          \u5176\u4e2d：<\/p>\n

                            \n
                          • \u03d5j(x)\u03d5j\u200b(x)：\u9884\u5148\u9009\u5b9a\u7684\u57fa\u51fd\u6570；<\/li>\n
                          • aj(t)aj\u200b(t)：\u9700\u8981\u6c42\u89e3\u7684\u7cfb\u6570；<\/li>\n
                          • UhUh\u200b：\u5bf9\u771f\u5b9e\u72b6\u6001\u7684\u8fd1\u4f3c\u3002<\/li>\n<\/ul>\n

                            \u4f8b\u5982，\u6700\u7b80\u5355\u7684\u7ebf\u6027\u5355\u5143，\u53ef\u4ee5\u901a\u8fc7\u7aef\u70b9\u503c\u5728\u5355\u5143\u5185\u90e8\u8fdb\u884c\u7ebf\u6027\u63d2\u503c\u3002<\/p>\n

                            \u968f\u540e，\u5c06\u5fae\u5206\u65b9\u7a0b\u4e58\u4ee5\u6d4b\u8bd5\u51fd\u6570\u5e76\u8fdb\u884c\u79ef\u5206，\u4f7f\u65b9\u7a0b\u5728\u8fd9\u79cd\u79ef\u5206\u610f\u4e49\u4e0b\u6210\u7acb\u3002\u8fd9\u79f0\u4e3a\u200b\u5f31\u5f62\u5f0f\u200b\u3002<\/p>\n

                            \u6709\u9650\u5143\u4e5f\u6709\u4e0d\u540c\u7c7b\u578b\u3002\u8fde\u7eed Galerkin \u6709\u9650\u5143\u901a\u5e38\u8981\u6c42\u76f8\u90bb\u5355\u5143\u7684\u89e3\u6ee1\u8db3\u76f8\u5e94\u8fde\u7eed\u6027；\u95f4\u65ad Galerkin（DG）\u5141\u8bb8\u5355\u5143\u4e4b\u95f4\u51fa\u73b0\u72b6\u6001\u8df3\u8dc3，\u56e0\u6b64\u540c\u6837\u9700\u8981\u6570\u503c\u754c\u9762\u901a\u91cf\u6765\u8fde\u63a5\u76f8\u90bb\u5355\u5143\u3002<\/p>\n

                            3.2.5 \u4e09\u79cd\u79bb\u6563\u65b9\u6cd5\u7684\u533a\u522b<\/h5>\n\n\u65b9\u6cd5\u5e38\u89c1\u672a\u77e5\u91cf\u8868\u793a\u5bf9\u5f53\u524d\u9879\u76ee\u7684\u4e3b\u8981\u8003\u8651<\/tr>\n\n\n\n\n
                            \u6709\u9650\u5dee\u5206<\/td>\n\u7f51\u683c\u70b9\u4e0a\u7684\u72b6\u6001\u503c<\/td>\n\u89c4\u5219\u7f51\u683c\u5b9e\u73b0\u76f4\u63a5，\u9002\u5408\u5148\u7406\u89e3\u5bfc\u6570\u548c\u6ce2\u52a8<\/td>\n<\/tr>\n
                            \u6709\u9650\u4f53\u79ef<\/td>\n\u5355\u5143\u5e73\u5747\u72b6\u6001<\/td>\n\u4fbf\u4e8e\u660e\u786e\u8ddf\u8e2a\u6c34\u91cf\u3001\u52a8\u91cf\u4ee5\u53ca\u533a\u57df\u4e4b\u95f4\u7684\u4ea4\u6362<\/td>\n<\/tr>\n
                            \u6709\u9650\u5143<\/td>\n\u57fa\u51fd\u6570\u7cfb\u6570<\/td>\n\u9002\u5408\u590d\u6742\u51e0\u4f55\u3001\u9ad8\u9636\u8fd1\u4f3c\u7b49\u9700\u6c42，\u5165\u95e8\u5b9e\u73b0\u66f4\u590d\u6742<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                            3.3 \u754c\u9762\u901a\u91cf<\/h4>\n

                            3.3.1 \u7269\u7406\u901a\u91cf\u548c\u6570\u503c\u901a\u91cf\u7684\u5173\u7cfb<\/h5>\n

                            \u7269\u7406\u6a21\u578b\u7ed9\u51fa\u4e86：<\/p>\n

                            F(U)=[huhu2+12gh2]
                            \nF(U) = \\\\begin{bmatrix} hu \\\\\\\\ hu^2 + \\\\frac{1}{2}gh^2 \\\\end{bmatrix}
                            \n<\/span><\/span>F<\/span>(<\/span>U<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>h<\/span>u<\/span><\/span><\/span><\/span>h<\/span>u<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>g<\/span>h<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                            \u4f46\u5728\u79bb\u6563\u7f51\u683c\u4e2d，\u540c\u4e00\u4e2a\u754c\u9762\u6709\u4e24\u4e2a\u6765\u6e90\u4e0d\u540c\u7684\u72b6\u6001：<\/p>\n

                            UL，UR
                            \nU_L，U_R
                            \n<\/span><\/span>U<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，<\/span>U<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                            \u5b83\u4eec\u5206\u522b\u6765\u81ea：<\/p>\n

                              \n
                            • \u5de6\u5355\u5143\u7684\u53f3\u8fb9\u754c；<\/li>\n
                            • \u53f3\u5355\u5143\u7684\u5de6\u8fb9\u754c\u3002<\/li>\n<\/ul>\n

                              \u4e24\u4fa7\u6c34\u6df1\u3001\u901f\u5ea6\u53ef\u80fd\u4e0d\u540c，\u56e0\u6b64：<\/p>\n

                              F(UL)\u2260F(UR)
                              \nF(U_L) \\\\neq F(U_R)
                              \n<\/span><\/span>F<\/span>(<\/span>U<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>F<\/span>(<\/span>U<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                              \u800c\u4e00\u4e2a\u5171\u4eab\u754c\u9762\u9700\u8981\u6709\u7edf\u4e00\u7684\u4ea4\u6362\u91cf，\u56e0\u6b64\u8981\u6839\u636e\u5de6\u53f3\u4e24\u4fa7\u72b6\u6001\u8ba1\u7b97：<\/p>\n

                              F\u203e=F(UL,UR)
                              \n\\\\overline{F} = \\\\mathcal F(U_L, U_R)
                              \n<\/span><\/span><\/span>F<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>F<\/span>(<\/span>U<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>U<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                              \u8fd9\u91cc：<\/p>\n

                                \n
                              • F：\u7531\u7269\u7406\u6a21\u578b\u89c4\u5b9a\u7684\u7269\u7406\u901a\u91cf；<\/li>\n
                              • \\\\mathcal F：\u9009\u62e9\u7684\u6570\u503c\u901a\u91cf\u7b97\u6cd5；<\/li>\n
                              • \\\\overline F：\u5b9e\u9645\u7528\u4e8e\u7f51\u683c\u66f4\u65b0\u7684\u754c\u9762\u901a\u91cf\u3002<\/li>\n<\/ul>\n
                                3.3.2 \u5c40\u90e8 Riemann \u95ee\u9898<\/h5>\n

                                \u53ef\u4ee5\u628a\u4e24\u4e2a\u5355\u5143\u4e4b\u95f4\u7684\u754c\u9762\u6682\u65f6\u770b\u6210\u4e00\u9053\u9694\u677f：<\/p>\n

                                  \n
                                • \u5de6\u4fa7\u5177\u6709\u72b6\u6001 UL；<\/li>\n
                                • \u53f3\u4fa7\u5177\u6709\u72b6\u6001 UR；<\/li>\n
                                • \u5728\u67d0\u4e00\u65f6\u523b\u79fb\u9664\u9694\u677f\u3002<\/li>\n<\/ul>\n

                                  \u968f\u540e\u4f1a\u4ea7\u751f\u6ce2，\u5e76\u5728\u754c\u9762\u9644\u8fd1\u5f62\u6210\u65b0\u7684\u6d41\u52a8\u72b6\u6001\u3002<\/p>\n

                                  \u8fd9\u79cd\u5de6\u53f3\u521d\u59cb\u72b6\u6001\u5404\u81ea\u4e3a\u5e38\u6570\u7684\u95ee\u9898，\u79f0\u4e3a \u200bRiemann \u95ee\u9898\u200b\u3002<\/p>\n

                                  \u7cbe\u786e\u6c42\u89e3\u5b83\u53ef\u4ee5\u5f97\u5230\u754c\u9762\u5904\u7684\u72b6\u6001\u548c\u901a\u91cf\u3002\u4f46\u5728\u5927\u91cf\u7f51\u683c\u3001\u6bcf\u4e2a\u65f6\u95f4\u6b65\u90fd\u8981\u8ba1\u7b97\u7684\u60c5\u51b5\u4e0b，\u901a\u5e38\u4f1a\u91c7\u7528\u8fd1\u4f3c\u6c42\u89e3\u5668\u3002<\/p>\n

                                  3.3.3 Rusanov：\u5e73\u5747\u7269\u7406\u901a\u91cf，\u52a0\u4e0a\u6570\u503c\u8017\u6563<\/h5>\n

                                  Rusanov \u901a\u91cf\u4e5f\u79f0\u5c40\u90e8 Lax-Friderichs \u901a\u91cf：<\/p>\n

                                  F^Rus=FL+FR2\u2212a2(UR\u2212UL)
                                  \n\\\\widehat F _{Rus} = \\\\frac{F_L + F_R}{2}-\\\\frac{a}{2}(U_R-U_L)
                                  \n<\/span><\/span><\/span>F<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>R<\/span>u<\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>F<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>F<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>U<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>U<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                  \u5176\u4e2d：<\/p>\n

                                  FL=F(UL)，FR=F(UR)
                                  \nF_L = F(U_L)，F_R = F(U_R)
                                  \n<\/span><\/span>F<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>F<\/span>(<\/span>U<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>，<\/span>F<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>F<\/span>(<\/span>U<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                  \u5bf9\u5168\u6e7f SWE，\u4e00\u79cd\u5e38\u89c1\u7684\u5c40\u90e8\u901f\u5ea6\u4f30\u8ba1\u4e3a：<\/p>\n

                                  a=max(\u2223uL\u2223+ghL，\u2223uR\u2223+ghR)
                                  \na = max \\\\left ( |u_L| + \\\\sqrt{gh_L}，|u_R| + \\\\sqrt{gh_R} \\\\right )
                                  \n<\/span><\/span>a<\/span><\/span>=<\/span><\/span><\/span><\/span>ma<\/span>x<\/span><\/span>(<\/span><\/span>\u2223<\/span>u<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span>+<\/span><\/span><\/span>g<\/span>h<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>，<\/span>\u2223<\/span>u<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span>+<\/span><\/span><\/span>g<\/span>h<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                  \u516c\u5f0f\u5206\u4e3a\u4e24\u90e8\u5206：<\/p>\n

                                  FL+FR2
                                  \n\\\\frac{F_L + F_R}{2}
                                  \n<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>F<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>F<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                  \u53d6\u4e24\u4fa7\u7269\u7406\u901a\u91cf\u7684\u5e73\u5747\u503c；<\/p>\n

                                  \u2212a2(UR\u2212UL)
                                  \n-\\\\frac{a}{2}(U_R-U_L)
                                  \n<\/span><\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>U<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>U<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                  \u6839\u636e\u72b6\u6001\u5dee\u5f02\u52a0\u5165\u6570\u503c\u8017\u6563\u3002<\/p>\n

                                  \u8fd9\u79cd\u8017\u6563\u6709\u52a9\u4e8e\u6291\u5236\u632f\u8361，\u4f46\u4e5f\u53ef\u80fd\u628a\u9661\u5ced\u53d8\u5316\u548c\u7ec6\u5c0f\u6ce2\u7eb9\u62b9\u5e73\u3002\u56e0\u6b64，Rusanov \u5b9e\u73b0\u7b80\u5355，\u4f46\u8ba1\u7b97\u51fa\u7684\u6ce2\u6d6a\u7ec6\u8282\u4e5f\u4e0e\u7f51\u683c\u5927\u5c0f\u3001\u91cd\u6784\u9636\u6570\u6709\u5173\u3002<\/p>\n

                                  \u4f8b\u5982，\u8bbe：<\/p>\n

                                  hL=2，hR=1uL=uR=0，g=9.81
                                  \nh_L = 2，h_R = 1 \\\\\\\\
                                  \nu_L = u_R = 0，g = 9.81
                                  \n<\/span><\/span>h<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span>，<\/span>h<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>u<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>u<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span>，<\/span>g<\/span><\/span>=<\/span><\/span><\/span><\/span>9.81<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                  \u5219：<\/p>\n

                                  UL=[20]，UR=[10]
                                  \nU_L = \\\\begin{bmatrix} 2 \\\\\\\\ 0 \\\\end{bmatrix}，U_R = \\\\begin{bmatrix} 1 \\\\\\\\ 0 \\\\end{bmatrix}
                                  \n<\/span><\/span>U<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span>，<\/span>U<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                  \u7269\u7406\u901a\u91cf\u4e3a：<\/p>\n

                                  FL=[019.62]，FR=[04.905]
                                  \nF_L = \\\\begin{bmatrix} 0 \\\\\\\\ 19.62 \\\\end{bmatrix}，F_R = \\\\begin{bmatrix} 0 \\\\\\\\ 4.905 \\\\end{bmatrix}
                                  \n<\/span><\/span>F<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>19.62<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span>，<\/span>F<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>0<\/span><\/span><\/span><\/span>4.905<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                  \u6700\u5927\u901f\u5ea6\u4f30\u8ba1：<\/p>\n

                                  a=9.81\u00d72\u22484.429
                                  \na = \\\\sqrt{9.81 \\\\times 2} \\\\approx 4.429
                                  \n<\/span><\/span>a<\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>9.81<\/span><\/span>\u00d7<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>4.429<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                  \u6700\u7ec8：<\/p>\n

                                  F^Rus\u2248[2.21512.263]
                                  \n\\\\widehat F_{Rus} \\\\approx \\\\begin{bmatrix} 2.215 \\\\\\\\ 12.263 \\\\end{bmatrix}
                                  \n<\/span><\/span><\/span>F<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>R<\/span>u<\/span>s<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>[<\/span><\/span><\/span>2.215<\/span><\/span><\/span><\/span>12.263<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                  \u7b2c\u4e00\u9879\u662f\u5355\u4f4d\u5bbd\u5ea6\u4f53\u79ef\u6d41\u91cf，\u6b63\u53f7\u8868\u793a\u5411\u53f3\u8f93\u6c34\u3002<\/p>\n

                                  \u5c3d\u7ba1\u4e24\u4fa7\u521d\u59cb\u901f\u5ea6\u90fd\u662f\u96f6，\u6c34\u6df1\u5dee\u5f15\u8d77\u7684\u538b\u529b\u4e0d\u5e73\u8861\u4ecd\u4f1a\u4ea7\u751f\u6d41\u52a8\u3002 \u6570\u503c\u901a\u91cf\u662f\u5728\u8fd1\u4f3c\u754c\u9762\u95ee\u9898\u968f\u5373\u53d1\u751f\u7684\u6f14\u5316\u3002<\/p>\n

                                  3.3.4 HLL：\u5206\u522b\u4f30\u8ba1\u5411\u5de6\u548c\u5411\u53f3\u7684\u6ce2\u901f<\/h5>\n

                                  HLL \u4f7f\u7528\u4e24\u4e2a\u6ce2\u901f：<\/p>\n

                                  SL，SR
                                  \nS_L，S_R
                                  \n<\/span><\/span>S<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，<\/span>S<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                  \u5206\u522b\u8868\u793a\u6700\u5de6\u4fa7\u548c\u6700\u53f3\u4fa7\u4f20\u64ad\u4fe1\u53f7\u7684\u901f\u5ea6\u4f30\u8ba1\u3002<\/p>\n

                                  \u5bf9\u5168\u6e7f SWE，\u4e00\u79cd\u57fa\u7840\u4f30\u8ba1\u662f：<\/p>\n

                                  SL=min(uL\u2212ghL，uR\u2212ghR)SL=max(uL+ghL，uR+ghR)
                                  \nS_L = min\\\\left ( u_L – \\\\sqrt{gh_L}，u_R – \\\\sqrt{gh_R} \\\\right ) \\\\\\\\
                                  \nS_L = max\\\\left ( u_L + \\\\sqrt{gh_L}，u_R + \\\\sqrt{gh_R} \\\\right )
                                  \n<\/span><\/span>S<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>min<\/span><\/span>(<\/span><\/span>u<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>g<\/span>h<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>，<\/span>u<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>g<\/span>h<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>S<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>ma<\/span>x<\/span><\/span>(<\/span><\/span>u<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span>g<\/span>h<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>，<\/span>u<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span>g<\/span>h<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                  \u5177\u4f53\u6c42\u89e3\u5668\u4e5f\u53ef\u80fd\u91c7\u7528\u66f4\u7a33\u5065\u7684\u901f\u5ea6\u4f30\u8ba1，\u5e72\u5e8a\u60c5\u51b5\u5c24\u5176\u9700\u8981\u4e13\u95e8\u5904\u7406\u3002<\/p>\n

                                  HLL \u901a\u91cf\u4e3a：<\/p>\n

                                  F^HLL={FL,SL\u22650SRFL\u2212SLFR+SLSR(UR\u2212UL)SR\u2212SL,SL<0<SRFR,SR\u22640
                                  \n\\\\widehat F_{HLL} =
                                  \n\\\\begin{cases}
                                  \nF_L, & S_L \\\\ge0 \\\\\\\\
                                  \n\\\\frac{S_R F_L – S_L F_R + S_L S_R(U_R – U_L)}{S_R-S_L}, & S_L < 0 < S_R \\\\\\\\
                                  \nF_R, & S_R \\\\le0
                                  \n\\\\end{cases}
                                  \n<\/span><\/span><\/span>F<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>H<\/span>LL<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>\u23a9<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u23a8<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u23a7<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>F<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span><\/span><\/span><\/span>S<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>S<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>S<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>F<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>S<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>F<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span>S<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>S<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>U<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span>U<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span><\/span>F<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>S<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2265<\/span><\/span>0<\/span><\/span><\/span><\/span>S<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><<\/span><\/span>0<\/span><\/span><<\/span><\/span>S<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>S<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2264<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                  \u5b83\u4f53\u73b0\u4e86\u4f20\u64ad\u65b9\u5411：<\/p>\n

                                    \n
                                  • \u5982\u679c\u6240\u6709\u4fe1\u53f7\u90fd\u5411\u53f3\u4f20\u64ad，\u754c\u9762\u7531\u5de6\u4fa7\u72b6\u6001\u51b3\u5b9a；<\/li>\n
                                  • \u5982\u679c\u6240\u6709\u4fe1\u53f7\u90fd\u5411\u5de6\u4f20\u64ad，\u754c\u9762\u7531\u53f3\u4fa7\u72b6\u6001\u51b3\u5b9a；<\/li>\n
                                  • \u5982\u679c\u4fe1\u53f7\u5411\u4e24\u4fa7\u4f20\u64ad，\u5c31\u4f7f\u7528\u4e2d\u95f4\u8868\u8fbe\u5f0f\u3002<\/li>\n<\/ul>\n

                                    HLL \u5c06\u4e24\u4e2a\u5916\u4fa7\u6ce2\u4e4b\u95f4\u7684\u590d\u6742\u7ed3\u6784\u8fd1\u4f3c\u4e3a\u4e00\u4e2a\u5e73\u5747\u72b6\u6001\u3002<\/p>\n

                                    Rusanov \u4e0e HLL \u8fd8\u6709\u4e00\u4e2a\u76f4\u63a5\u5173\u7cfb\u3002\u4ee4：<\/p>\n

                                    SL=\u2212a，SR=a
                                    \nS_L = -a，S_R = a
                                    \n<\/span><\/span>S<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span>a<\/span>，<\/span>S<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                    HLL \u5c31\u4f1a\u5316\u7b80\u6210 Rusanov \u901a\u91cf\u3002<\/p>\n

                                    \u6240\u4ee5，\u200bHLL \u5e76\u4e0d\u4fdd\u8bc1\u5728\u6bcf\u4e00\u79cd\u72b6\u6001\u4e0b\u90fd\u6bd4 Rusanov \u66f4\u7cbe\u7ec6\u200b；\u91c7\u7528\u5bf9\u79f0\u901f\u5ea6\u4f30\u8ba1\u65f6，\u4e24\u8005\u53ef\u4ee5\u5b8c\u5168\u76f8\u540c\u3002<\/p>\n

                                    3.3.5 Roe：\u5206\u89e3\u4e0d\u540c\u7684\u6ce2，\u518d\u5206\u522b\u5904\u7406\u4f20\u64ad<\/h5>\n

                                    Roe \u7684\u601d\u8def\u662f：\u5728\u754c\u9762\u9644\u8fd1\u6784\u9020\u4e00\u4e2a\u5177\u6709\u7279\u5b9a\u5b88\u6052\u6027\u8d28\u7684\u5c40\u90e8\u7ebf\u6027\u7cfb\u7edf，\u7528\u5b83\u8fd1\u4f3c\u539f\u6765\u7684\u975e\u7ebf\u6027\u95ee\u9898\u3002<\/p>\n

                                    \u5bf9\u4e00\u7ef4 SWE，\u5e38\u7528 Roe \u5e73\u5747\u4e3a：<\/p>\n

                                    u~=uLhL+uRhRhL+hRh~=hL+hR2，c~=gh~
                                    \n\\\\widetilde u = \\\\frac{u_L \\\\sqrt{h_L} + u_R{\\\\sqrt{h_R}}}{\\\\sqrt{h_L} + \\\\sqrt{h_R}} \\\\\\\\
                                    \n\\\\widetilde h = \\\\frac{h_L + h_R}{2}，\\\\widetilde c = \\\\sqrt{g\\\\widetilde h}
                                    \n<\/span><\/span><\/span>u<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span>h<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>u<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>u<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>h<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，<\/span><\/span>c<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>g<\/span><\/span>h<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                    \u4e24\u4e2a\u7279\u5f81\u901f\u5ea6\u4e3a：<\/p>\n

                                    \u03bb~1=u~\u2212c~，\u03bb~2=u~+c~
                                    \n\\\\widetilde \\\\lambda_1 = \\\\widetilde u – \\\\widetilde c，\\\\widetilde \\\\lambda_2 = \\\\widetilde u + \\\\widetilde c
                                    \n<\/span><\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>u<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>c<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>，<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>u<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span>c<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                    \u628a\u72b6\u6001\u5dee\u5206\u89e3\u6210\u4e24\u4e2a\u6ce2：<\/p>\n

                                    UR\u2212UL=\u03b11r1+\u03b12r2
                                    \nU_R – U_L = \\\\alpha_1 \\\\boldsymbol r_1 + \\\\alpha_2\\\\boldsymbol r_2
                                    \n<\/span><\/span>U<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>U<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u03b1<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>r<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b1<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>r<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                    \u518d\u8ba1\u7b97：<\/p>\n

                                    F^Roe=FL+FR2\u221212\u2211p=12\u2223\u03bb~p\u2223\u03b1prp
                                    \n\\\\widehat F_{Roe} = \\\\frac{F_L + F_R}{2} – \\\\frac{1}{2}\\\\sum_{p=1}^{2}|\\\\widetilde \\\\lambda_p| \\\\alpha_p \\\\boldsymbol r_p
                                    \n<\/span><\/span><\/span>F<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>R<\/span>oe<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>F<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>F<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>p<\/span>=<\/span>1<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span>\u03bb<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span>\u03b1<\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>r<\/span><\/span><\/span><\/span>p<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                    \u53ef\u4ee5\u628a\u5b83\u7406\u89e3\u4e3a：\u6bcf\u4e00\u79cd\u6ce2\u6309\u7167\u81ea\u5df1\u7684\u4f20\u64ad\u901f\u5ea6\u63d0\u4f9b\u76f8\u5e94\u7684\u6570\u503c\u8017\u6563\u3002<\/p>\n

                                    Roe \u80fd\u8f83\u7ec6\u81f4\u5730\u5904\u7406\u6ce2\u7ed3\u6784，\u4f46\u6807\u51c6 Roe \u65b9\u6cd5\u8fd8\u5b58\u5728\u9700\u8981\u5904\u7406\u7684\u95ee\u9898，\u4f8b\u5982\u8de8\u58f0\u901f\u7a00\u758f\u6ce2\u7684\u71b5\u4fee\u6b63，\u4ee5\u53ca\u67d0\u4e9b\u72b6\u6001\u4e0b\u51fa\u73b0\u975e\u7269\u7406\u8d1f\u6c34\u6df1\u3002<\/p>\n

                                    3.3.6 \u4e09\u79cd\u901a\u91cf\u5e94\u600e\u6837\u6bd4\u8f83<\/h5>\n\n\u901a\u91cf\u6838\u5fc3\u505a\u6cd5\u4e3b\u8981\u8003\u8651<\/tr>\n\n\n\n\n
                                    Rusanov\u9c81\u8428\u8bfa\u592b<\/td>\n\u4e00\u4e2a\u6700\u5927\u4f20\u64ad\u901f\u5ea6\u63a7\u5236\u8017\u6563<\/td>\n\u7b80\u5355，\u9002\u5408\u4f5c\u4e3a\u57fa\u7840\u5b9e\u73b0；\u8017\u6563\u53ef\u80fd\u8f83\u5927<\/td>\n<\/tr>\n
                                    HLL<\/td>\n\u4f7f\u7528\u5de6\u53f3\u4e24\u4e2a\u4f20\u64ad\u901f\u5ea6<\/td>\n\u4f53\u73b0\u4f20\u64ad\u65b9\u5411，\u7a33\u5065\u6027\u4f9d\u8d56\u901f\u5ea6\u4f30\u8ba1\u7b49\u914d\u5957\u5904\u7406<\/td>\n<\/tr>\n
                                    Roe<\/td>\n\u5bf9\u4e0d\u540c\u7279\u5f81\u6ce2\u5206\u522b\u5904\u7406<\/td>\n\u6ce2\u7ed3\u6784\u5206\u8fa8\u8f83\u7ec6，\u9700\u8981\u71b5\u4fee\u6b63\u3001\u6b63\u6c34\u6df1\u7b49\u5904\u7406<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                                    \u200b\u4e00\u4e2a\u5355\u5143\u754c\u9762\u7684\u5e73\u5747\u6c34\u9762\u662f\u5e73\u7684，\u4e5f\u4e0d\u610f\u5473\u7740\u52a8\u91cf\u901a\u91cf\u4e3a\u96f6\u200b\u3002\u9759\u6c34\u4e2d\u4ecd\u6709\u538b\u529b\u901a\u91cf；\u9759\u6b62\u72b6\u6001\u4f9d\u9760\u4e24\u4fa7\u538b\u529b\u4f5c\u7528\u76f8\u4e92\u62b5\u6d88\u6765\u4fdd\u6301\u3002<\/p>\n

                                    3.4 \u65f6\u95f4\u63a8\u8fdb<\/h4>\n

                                    3.4.1 \u7a7a\u95f4\u79bb\u6563\u540e，\u5f97\u5230\u7684\u662f\u53d8\u5316\u7387<\/h5>\n

                                    \u5b8c\u6210\u7a7a\u95f4\u79bb\u6563\u548c\u901a\u91cf\u8ba1\u7b97\u540e，\u53ef\u4ee5\u5199\u51fa：<\/p>\n

                                    dU\u203eidt=Li(U\u203e)
                                    \n\\\\frac{d\\\\overline{\\\\boldsymbol U}_i}{dt} = \\\\mathcal L_i(\\\\overline{\\\\boldsymbol U})
                                    \n<\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span><\/span><\/span><\/span><\/span>d<\/span><\/span>U<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>L<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>U<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                    \u5176\u4e2d：<\/p>\n

                                    Li(U\u203e)=\u2212F^i+12\u2212F^i\u221212\u0394x+S\u203ei
                                    \n\\\\mathcal L_i(\\\\overline{\\\\boldsymbol U}) = -\\\\frac{ \\\\widehat{\\\\boldsymbol F}_{i+\\\\frac12} – \\\\widehat{\\\\boldsymbol F}_{i-\\\\frac12} }{\\\\Delta x} + \\\\overline{\\\\boldsymbol S}_i
                                    \n<\/span><\/span>L<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span><\/span>U<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>\u0394<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>F<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>+<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>F<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>\u2212<\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span>S<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                    \\\\mathcal L \u662f\u79bb\u6563\u7a7a\u95f4\u7b97\u5b50，\u5b83\u8d1f\u8d23\u6839\u636e\u5f53\u524d\u72b6\u6001\u8ba1\u7b97：<\/p>\n

                                      \n
                                    • \u5404\u754c\u9762\u7684\u6d41\u52a8；<\/li>\n
                                    • \u5355\u5143\u5185\u6c34\u6df1\u7684\u53d8\u5316\u7387；<\/li>\n
                                    • \u5355\u5143\u5185\u52a8\u91cf\u7684\u53d8\u5316\u7387；<\/li>\n
                                    • \u5fc5\u8981\u7684\u6e90\u9879\u4f5c\u7528\u3002<\/li>\n<\/ul>\n

                                      \u6b64\u65f6，\u6574\u4e2a\u95ee\u9898\u6210\u4e3a\u4e00\u7ec4\u5173\u4e8e\u65f6\u95f4\u7684\u5e38\u5fae\u5206\u65b9\u7a0b\u3002<\/p>\n

                                      \u65f6\u95f4\u63a8\u8fdb\u65b9\u6cd5\u51b3\u5b9a：\u5982\u4f55\u5229\u7528\u8fd9\u4e9b\u53d8\u5316\u7387，\u628a\u5f53\u524d\u72b6\u6001\u63a8\u8fdb\u5230\u4e0b\u4e00\u65f6\u523b\u3002<\/p>\n

                                      \u8fd9\u79cd\u5148\u79bb\u6563\u7a7a\u95f4\u3001\u518d\u6c42\u89e3\u65f6\u95f4\u53d8\u5316\u7684\u65b9\u6cd5\u901a\u5e38\u79f0\u4e3a\u7ebf\u65b9\u6cd5\u3002<\/p>\n

                                      3.4.2 \u663e\u5f0f Euler：\u4f7f\u7528\u5f53\u524d\u53d8\u5316\u7387\u524d\u8fdb\u4e00\u6b65<\/h5>\n

                                      \u663e\u793a Euler \u4e3a：<\/p>\n

                                      U(n+1)=Un+\u0394tL(Un)
                                      \nU^(n+1) = U^n + \\\\Delta t \\\\mathcal L(U^n)
                                      \n<\/span><\/span>U<\/span><\/span>(<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>n<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>U<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u0394<\/span>t<\/span>L<\/span>(<\/span>U<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                      \u542b\u4e49\u662f：\u5047\u8bbe\u5728\u8fd9\u4e00\u4e2a\u77ed\u65f6\u95f4\u6bb5\u5185，\u72b6\u6001\u6309\u7167\u5f53\u524d\u53d8\u5316\u7387\u53d8\u5316\u3002\u5b83\u53ea\u8ba1\u7b97\u4e00\u6b21\u7a7a\u95f4\u7b97\u5b50，\u5f62\u5f0f\u6700\u7b80\u5355，\u65f6\u95f4\u7cbe\u5ea6\u4e3a\u4e00\u9636\u3002<\/p>\n

                                      \u4f7f\u7528 3.3.3 \u4e2d\u7684\u4f8b\u5b50，\u8bbe\u4e24\u4e2a\u5355\u5143\u5bbd\u5ea6\u5747\u4e3a：<\/p>\n

                                      \u0394x=1m
                                      \n\\\\Delta x = 1 m
                                      \n<\/span><\/span>\u0394<\/span>x<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                      \u5b83\u4eec\u4e4b\u95f4\u7684\u4f53\u79ef\u901a\u91cf\u7ea6\u4e3a：<\/p>\n

                                      F^h=2.215m2\/s
                                      \n\\\\widehat F_h = 2.215 m^2\/s
                                      \n<\/span><\/span><\/span>F<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>2.215<\/span>m<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\/<\/span>s<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                      \u82e5\u5916\u4fa7\u8fb9\u754c\u6ca1\u6709\u6c34\u6d41\u901a\u8fc7，\u53d6：<\/p>\n

                                      \u0394t=0.05s
                                      \n\\\\Delta t = 0.05s
                                      \n<\/span><\/span>\u0394<\/span>t<\/span><\/span>=<\/span><\/span><\/span><\/span>0.05<\/span>s<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                      \u5219\u5de6\u5355\u5143\u6c34\u6df1\u51cf\u5c11：<\/p>\n

                                      \u0394hL=\u2212\u0394t\u0394xF^h\u2248\u22120.1107m
                                      \n\\\\Delta h_L = – \\\\frac{\\\\Delta t}{\\\\Delta x}\\\\widehat F_h \\\\approx -0.1107m
                                      \n<\/span><\/span>\u0394<\/span>h<\/span><\/span>L<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>\u0394<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u0394<\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>F<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>h<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>\u2212<\/span>0.1107<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                      \u53f3\u5355\u5143\u589e\u52a0\u76f8\u540c\u6c34\u6df1：<\/p>\n

                                      \u0394hR\u2248+0.1107m
                                      \n\\\\Delta h_R \\\\approx +0.1107m
                                      \n<\/span><\/span>\u0394<\/span>h<\/span><\/span>R<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>+<\/span>0.1107<\/span>m<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                      \u4e8e\u662f：<\/p>\n

                                      hLn+1\u22481.8893hRn+1\u22481.1107
                                      \nh_L^{n+1} \\\\approx 1.8893 \\\\\\\\
                                      \nh_R^{n+1} \\\\approx 1.1107
                                      \n<\/span><\/span>h<\/span><\/span>L<\/span><\/span><\/span><\/span>n<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>1.8893<\/span><\/span><\/span><\/span>h<\/span><\/span>R<\/span><\/span><\/span><\/span>n<\/span>+<\/span>1<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>1.1107<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                      \u8fd9\u91cc\u5c55\u793a\u4e86\u8d28\u91cf\u5206\u91cf；\u5b9e\u9645\u6c42\u89e3\u5668\u8fd8\u5fc5\u987b\u540c\u6b65\u66f4\u65b0\u52a8\u91cf\u5206\u91cf\u3002<\/p>\n

                                      4.2.3 Runge-Kutta：\u5728\u4e00\u4e2a\u65f6\u95f4\u6b65\u5185\u591a\u6b21\u8bc4\u4f30\u53d8\u5316\u7387<\/h5>\n

                                      Runge\u2013Kutta \u662f\u4e00\u7c7b\u65b9\u6cd5\u7684\u7edf\u79f0\u3002\u5b83\u901a\u8fc7\u6784\u9020\u4e2d\u95f4\u72b6\u6001，\u591a\u6b21\u8bc4\u4f30\u53d8\u5316\u7387，\u518d\u7ec4\u5408\u5f97\u5230\u4e0b\u4e00\u65f6\u523b\u7684\u7ed3\u679c\u3002<\/p>\n

                                      \u5e38\u89c1\u7684\u4e8c\u9636 SSP Runge\u2013Kutta \u4e3a：<\/p>\n

                                      U(1)=Un+\u0394tL(Un)U(n+1)=12Un+12[U(1)+\u0394tL(U(1))]
                                      \nU^{(1)}=U^n+\\\\Delta t\\\\mathcal L(U^n) \\\\\\\\
                                      \nU^{(n+1)}=\\\\frac{1}{2}U^n+\\\\frac{1}{2}\\\\left [ U^{(1)}+\\\\Delta t \\\\mathcal L(U^{(1)}) \\\\right ]
                                      \n<\/span><\/span>U<\/span><\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>U<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u0394<\/span>t<\/span>L<\/span>(<\/span>U<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>U<\/span><\/span>(<\/span>n<\/span>+<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>U<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span>U<\/span><\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u0394<\/span>t<\/span>L<\/span>(<\/span>U<\/span><\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                      \u7b2c\u4e00\u9636\u6bb5\u5f97\u5230\u9884\u6d4b\u72b6\u6001；\u7b2c\u4e8c\u9636\u6bb5\u91cd\u65b0\u8ba1\u7b97\u9884\u6d4b\u72b6\u6001\u4e0b\u7684\u53d8\u5316\u7387，\u518d\u8fdb\u884c\u7ec4\u5408\u3002\u7b2c\u4e8c\u9636\u6bb5\u5fc5\u987b\u91cd\u65b0\u8ba1\u7b97\u901a\u91cf\u3002<\/p>\n

                                      4.2.4 SSPRK3 \u4e0e\u201c\u5f3a\u7a33\u5b9a\u4fdd\u6301\u201d<\/h5>\n

                                      \u4e09\u9636 SSP Runge-Kutta \u7684\u5e38\u89c1\u5f62\u5f0f\u4e3a：<\/p>\n

                                      U(1)=Un+\u0394tL(Un)U(2)=34Un+14[U(1)+\u0394tL(U(1))]U(n+1)=13Un+23[U(2)+\u0394tL(U(2))]
                                      \nU^{(1)}=U^n+\\\\Delta t\\\\mathcal L(U^n) \\\\\\\\
                                      \nU^{(2)}=\\\\frac{3}{4}U^n+\\\\frac{1}{4}\\\\left [ U^{(1)}+\\\\Delta t \\\\mathcal L(U^{(1)}) \\\\right ] \\\\\\\\
                                      \nU^{(n+1)}=\\\\frac{1}{3}U^n+\\\\frac{2}{3}\\\\left [ U^{(2)}+\\\\Delta t \\\\mathcal L(U^{(2)}) \\\\right ]
                                      \n<\/span><\/span>U<\/span><\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>U<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u0394<\/span>t<\/span>L<\/span>(<\/span>U<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span>U<\/span><\/span>(<\/span>2<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>U<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span>U<\/span><\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u0394<\/span>t<\/span>L<\/span>(<\/span>U<\/span><\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span>U<\/span><\/span>(<\/span>n<\/span>+<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>U<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span><\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span>U<\/span><\/span>(<\/span>2<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>\u0394<\/span>t<\/span>L<\/span>(<\/span>U<\/span><\/span>(<\/span>2<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                      \u5b83\u9700\u8981\u4e09\u6b21\u7a7a\u95f4\u7b97\u5b50\u8bc4\u4f30\u3002<\/p>\n

                                      SSP \u7684\u542b\u4e49\u662f：\u5982\u679c\u7a7a\u95f4\u79bb\u6563\u4e0e\u524d\u5411 Euler \u5728\u4e00\u5b9a\u6b65\u957f\u9650\u5236\u4e0b\u5177\u6709\u67d0\u79cd\u5408\u9002\u7684\u7a33\u5b9a\u6027\u8d28，SSP \u65f6\u95f4\u65b9\u6cd5\u53ef\u4ee5\u5728\u76f8\u5e94\u9650\u5236\u4e0b\u4fdd\u7559\u8be5\u6027\u8d28\u3002\u5b83\u4e0d\u80fd\u81ea\u52a8\u4fee\u590d\u672c\u6765\u5c31\u4e0d\u7a33\u5b9a\u6216\u4f1a\u4ea7\u751f\u8d1f\u6c34\u6df1\u7684\u7a7a\u95f4\u79bb\u6563\u3002<\/p>\n

                                      3.2.5 \u4e09\u79cd\u79bb\u6563\u65b9\u5f0f\u7684\u533a\u522b<\/h5>\n\n\u65b9\u6cd5\u65f6\u95f4\u9636\u6570\u6bcf\u6b65\u7a7a\u95f4\u7b97\u5b50\u8bc4\u4f30\u6b21\u6570<\/tr>\n\n\n\n\n\n
                                      \u663e\u5f0f Euler<\/td>\n1<\/td>\n1<\/td>\n<\/tr>\n
                                      SSPRK2<\/td>\n2<\/td>\n2<\/td>\n<\/tr>\n
                                      SSPRK3<\/td>\n3<\/td>\n3<\/td>\n<\/tr>\n
                                      \u7ecf\u5178 RK4<\/td>\n4<\/td>\n4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                                      \u65f6\u95f4\u9636\u6570\u66f4\u9ad8，\u5e76\u4e0d\u81ea\u52a8\u610f\u5473\u7740\u66f4\u9002\u5408\u4f60\u7684\u5b9e\u73b0\u3002\u8fd8\u9700\u8981\u8003\u8651\u7a33\u5b9a\u6027\u3001\u7a7a\u95f4\u8bef\u5dee\u3001\u663e\u5b58\u8bbf\u95ee\u548c\u603b\u8ba1\u7b97\u6210\u672c\u3002<\/p>\n

                                      3.2.6 \u65f6\u95f4\u7cbe\u5ea6\u4e0e\u7a7a\u95f4\u7cbe\u5ea6\u7684\u8026\u5408<\/h5>\n

                                      \u5047\u8bbe\u7a7a\u95f4\u79bb\u6563\u53ea\u6709\u4e00\u9636，\u800c\u65f6\u95f4\u63a8\u8fdb\u4f7f\u7528\u56db\u9636 RK，\u6574\u4f53\u8bef\u5dee\u4ecd\u53ef\u80fd\u4e3b\u8981\u6765\u81ea\u7a7a\u95f4\u79bb\u6563：<\/p>\n

                                      \u8bef\u5dee\u223cCx\u0394x+Ct\u0394t4
                                      \n\u8bef\u5dee \\\\sim C_x \\\\Delta x + C_t \\\\Delta t^4
                                      \n<\/span><\/span>\u8bef\u5dee<\/span><\/span>\u223c<\/span><\/span><\/span><\/span>C<\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u0394<\/span>x<\/span><\/span>+<\/span><\/span><\/span><\/span>C<\/span><\/span>t<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u0394<\/span>t<\/span><\/span>4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                      \u8fd9\u662f\u5e73\u6ed1\u89e3\u6761\u4ef6\u4e0b\u7684\u793a\u610f\u5173\u7cfb\u3002<\/p>\n

                                      \u56e0\u6b64：<\/p>\n

                                        \n
                                      • \u4e00\u9636\u7a7a\u95f4\u65b9\u6cd5\u52a0\u9ad8\u9636\u65f6\u95f4\u65b9\u6cd5，\u4e0d\u80fd\u81ea\u52a8\u6062\u590d\u88ab\u7a7a\u95f4\u8017\u6563\u62b9\u6389\u7684\u6ce2\u7eb9；<\/li>\n
                                      • \u9ad8\u9636\u7a7a\u95f4\u65b9\u6cd5\u52a0\u8fc7\u4e8e\u7c97\u7cd9\u7684\u65f6\u95f4\u63a8\u8fdb，\u4e5f\u53ef\u80fd\u635f\u5931\u7cbe\u5ea6；<\/li>\n
                                      • \u5b58\u5728\u95f4\u65ad\u65f6，\u5c40\u90e8\u7cbe\u5ea6\u8fd8\u4f1a\u53d7\u5230\u9650\u5236\u5668\u7b49\u56e0\u7d20\u5f71\u54cd\u3002<\/li>\n<\/ul>\n

                                        \u4e00\u4e2a\u5e38\u89c1\u7684\u5347\u7ea7\u65b9\u5411\u662f：\u5148\u5efa\u7acb\u4e00\u9636\u6709\u9650\u4f53\u79ef\u4e0e\u663e\u5f0f Euler \u57fa\u7ebf，\u518d\u589e\u52a0\u53d7\u9650\u7ebf\u6027\u91cd\u6784\u548c SSPRK2\u3002<\/p>\n

                                        3.2.7 \u65f6\u95f4\u6b65\u957f\u7684\u7a33\u5b9a\u6027\u8981\u6c42<\/h5>\n

                                        \u5bf9\u5e38\u89c1\u4e00\u7ef4\u663e\u5f0f\u683c\u5f0f，CFL \u6761\u4ef6\u5177\u6709\u5982\u4e0b\u5f62\u5f0f：<\/p>\n

                                        \u0394t\u2264CCFL\u0394xmaxi(\u2223ui\u2223+ghi)
                                        \n\\\\Delta t \\\\leq C_{CFL}\\\\frac{\\\\Delta x}{max_i(|u_i|+\\\\sqrt{gh_i})}
                                        \n<\/span><\/span>\u0394<\/span>t<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>C<\/span><\/span>C<\/span>F<\/span>L<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>ma<\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>\u2223<\/span>u<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2223<\/span><\/span>+<\/span><\/span><\/span>g<\/span>h<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u0394<\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                        \u8fd9\u91cc\u7684 Ccfl \u4e0a\u9650\u4f9d\u8d56\u5177\u4f53\u683c\u5f0f\u3002\u5bf9\u4e8e\u663e\u5f0f Euler \u65f6\u95f4\u63a8\u8fdb，\u4e00\u7ef4\u60c5\u51b5\u4e0b \u200bCmax=1；\u4f46\u5728\u591a\u7ef4\u6216\u9ad8\u9636\u683c\u5f0f\u4e0b，\u901a\u5e38\u53d6 0.5\u223c0.9 \u200b\u4ee5\u786e\u4fdd\u5b89\u5168\u3002<\/p>\n

                                        \u4e8c\u7ef4\u975e\u5206\u88c2\u683c\u5f0f\u5e38\u89c1\u7684\u4fdd\u5b88\u6b65\u957f\u5f62\u5f0f\u4e3a：<\/p>\n

                                        \u0394t\u2264CCFLax\u0394x+az\u0394z
                                        \n\\\\Delta t \\\\leq \\\\frac{C_{CFL}}{\\\\frac{a_x}{\\\\Delta x}+\\\\frac{a_z}{\\\\Delta z}}
                                        \n<\/span><\/span>\u0394<\/span>t<\/span><\/span>\u2264<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u0394<\/span>x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>x<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u0394<\/span>z<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>a<\/span><\/span>z<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>C<\/span><\/span>C<\/span>F<\/span>L<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                                        \u5176\u4e2d ax, az \u662f\u4e24\u4e2a\u65b9\u5411\u7684\u6700\u5927\u4f20\u64ad\u901f\u5ea6\u4f30\u8ba1\u3002<\/p>\n

                                        CFL \u7ea6\u675f\u5c06\u524d\u9762\u5404\u5c42\u8054\u7cfb\u8d77\u6765：\u7269\u7406\u6a21\u578b\u51b3\u5b9a\u4f20\u64ad\u901f\u5ea6，\u7a7a\u95f4\u7f51\u683c\u51b3\u5b9a\u4fe1\u606f\u9700\u8981\u8de8\u8d8a\u7684\u8ddd\u79bb，\u65f6\u95f4\u65b9\u6cd5\u5f71\u54cd\u5141\u8bb8\u7684\u7a33\u5b9a\u6b65\u957f\u3002\u663e\u5f0f SWE \u6c42\u89e3\u5668\u901a\u5e38\u636e\u6b64\u9009\u62e9\u65f6\u95f4\u6b65\u3002<\/p>\n

                                        \u5bf9\u4e8e\u4e8c\u7ef4\u89c4\u5219\u7f51\u683c，\u5982\u679c\u5176\u4ed6\u6761\u4ef6\u4e0d\u53d8，\u5c06\u4e24\u4e2a\u65b9\u5411\u7684\u7f51\u683c\u95f4\u8ddd\u90fd\u51cf\u534a：<\/p>\n

                                          \n
                                        • \u5355\u5143\u603b\u6570\u7ea6\u589e\u52a0\u5230 4 \u500d；<\/li>\n
                                        • \u663e\u5f0f\u65f6\u95f4\u6b65\u901a\u5e38\u4e5f\u9700\u8981\u51cf\u534a；<\/li>\n
                                        • \u6a21\u62df\u540c\u6837\u7269\u7406\u65f6\u957f\u7684\u57fa\u7840\u8ba1\u7b97\u91cf\u53ef\u80fd\u63a5\u8fd1 8 \u500d\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

                                          \u4e8c\u3001SWE \u7684\u8fd0\u52a8\u673a\u5236
                                          \nSWE \u7684\u8fd0\u52a8\u673a\u5236\u53ef\u4ee5\u7406\u89e3\u6210：\u6c34\u9762\u5761\u5ea6\u6539\u53d8\u6d41\u901f，\u6d41\u52a8\u7684\u6c47\u805a\u548c\u53d1\u6563\u6539\u53d8\u6c34\u6df1\u3002
                                          \n\u5047\u8bbe\u4f60\u5728\u5e73\u9759\u6c34\u9762\u4e2d\u592e\u5236\u9020\u4e00\u4e2a\u9686\u8d77：
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