\n| \u5c40\u90e8\u5c3a\u5ea6\u4e0e\u8fc7\u6e21<\/td>\n | \u5224\u65ad\u8fd1\u58c1\u68af\u5ea6\u7b49\u80fd\u5426\u5408\u7406\u5206\u8fa8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \u975e\u6b63\u4ea4\u6027\u548c\u504f\u659c\u4e0d\u662f\u540c\u4e00\u4e2a\u91cf\u3002\u5355\u5143\u957f\u5bbd\u6bd4\u5927，\u4e5f\u4e0d\u80fd\u8131\u79bb\u6d41\u52a8\u65b9\u5411\u3001\u68af\u5ea6\u548c\u79bb\u6563\u683c\u5f0f，\u76f4\u63a5\u5224\u5b9a\u4e0d\u53ef\u7528\u3002<\/p>\n OpenFOAM\u63d0\u4f9bcheckMesh\u68c0\u67e5\u7f51\u683c\u6709\u6548\u6027，\u5b9e\u9645\u65e5\u5fd7\u5e94\u4e0e\u8f6f\u4ef6\u7248\u672c\u548c\u8bbe\u7f6e\u4e00\u8d77\u4fdd\u5b58\u3002Foundation v13\u7f51\u683c\u5de5\u5177\u8bf4\u660e<\/p>\n \u4f46\u8981\u6ce8\u610f：<\/p>\n checkMesh\u901a\u8fc7，\u4e0d\u7b49\u4e8e\u8fb9\u754c\u6761\u4ef6\u6b63\u786e，\u4e5f\u4e0d\u7b49\u4e8e\u5df2\u7ecf\u8fbe\u5230\u7f51\u683c\u65e0\u5173\u3002<\/p>\n \u672c\u8282\u4e0d\u63d0\u4f9b\u9002\u7528\u4e8e\u6240\u6709\u6a21\u578b\u7684\u7edf\u4e00\u7f51\u683c\u8d28\u91cf\u9608\u503c\u3002<\/p>\n \u56db\u3001\u5165\u53e3\u548c\u51fa\u53e3\u6761\u4ef6，\u8981\u6210\u7ec4\u7406\u89e3<\/h3>\n\u8981\u5b9e\u73b0\u5e73\u884c\u677f\u5145\u5206\u53d1\u5c55\u6d41\u52a8，\u53ef\u4ee5\u91c7\u7528\u4e0d\u540c\u8def\u5f84，\u4f46\u4e0d\u80fd\u968f\u610f\u6df7\u642d\u3002<\/p>\n 4.1 \u901f\u5ea6\u6216\u6d41\u91cf\u9a71\u52a8<\/h4>\n\u5165\u53e3\u7ed9\u5b9a\u901f\u5ea6\u5256\u9762\u6216\u6d41\u91cf，\u51fa\u53e3\u8bbe\u7f6e\u538b\u529b\u53c2\u8003，\u5176\u4ed6\u53d8\u91cf\u91c7\u7528\u4e0e\u6c42\u89e3\u5668\u76f8\u5bb9\u7684\u6761\u4ef6\u3002<\/p>\n \u5982\u679c\u7ed9\u5b9a\u5747\u5300\u5165\u53e3，\u901a\u5e38\u4f1a\u5b58\u5728\u53d1\u5c55\u6bb5，\u4e0d\u80fd\u8981\u6c42\u6574\u4e2a\u901a\u9053\u7acb\u5373\u6ee1\u8db3\u5145\u5206\u53d1\u5c55\u629b\u7269\u7ebf\u5256\u9762\u3002<\/p>\n \u90e8\u5206\u6559\u7a0b\u91c7\u7528\u5165\u53e3\u538b\u529bzeroGradient\u3001\u51fa\u53e3\u901f\u5ea6zeroGradient\u7b49\u7ec4\u5408，\u4f46\u8fd9\u4e0d\u80fd\u76f4\u63a5\u8bc1\u660e\u6574\u4e2a\u89e3\u6790\u573a\u4e0e\u8be5\u6570\u503c\u6848\u4f8b\u4e25\u683c\u4e00\u81f4，\u4ecd\u9700\u68c0\u67e5\u5165\u53e3\u3001\u51fa\u53e3\u5f71\u54cd\u548c\u6bd4\u8f83\u4f4d\u7f6e\u3002<\/p>\n 4.2 \u538b\u529b\u9a71\u52a8<\/h4>\n\u89c4\u5b9a\u5408\u9002\u7684\u538b\u529b\u9a71\u52a8，\u8ba9\u901f\u5ea6\u901a\u8fc7\u52a8\u91cf\u65b9\u7a0b\u548c\u76f8\u5bb9\u8fb9\u754c\u6761\u4ef6\u6c42\u51fa\u3002<\/p>\n \u4e0d\u8981\u53c8\u4efb\u610f\u6307\u5b9a\u4e00\u4e2a\u72ec\u7acb\u5165\u53e3\u6d41\u91cf，\u8981\u6c42\u4e24\u8005\u540c\u65f6\u6210\u7acb\u3002<\/p>\n 4.3 \u5468\u671f\u9a71\u52a8<\/h4>\n\u6d41\u5411\u4e24\u7aef\u91c7\u7528\u5339\u914d\u7684\u5468\u671f\u8bbe\u7f6e，\u5e76\u901a\u8fc7\u76f8\u5e94\u6e90\u9879\u6216\u5e73\u5747\u6d41\u52a8\u9a71\u52a8\u5b9e\u73b0\u76ee\u6807\u3002<\/p>\n \u4ec5\u4ec5\u5199\u4e0acyclic，\u4e0d\u4f1a\u81ea\u52a8\u4ea7\u751f\u4e0a\u4e00\u8282\u7684：<\/p>\n \\\\[ G=2\\\\ \\\\mathrm{Pa\/m}. \\\\]<\/p>\n \u8fb9\u754c\u662f\u5426\u9002\u5b9a，\u53d6\u51b3\u4e8e\u6574\u7ec4\u8bbe\u7f6e\u3001\u65b9\u7a0b\u548c\u7b97\u6cd5，\u4e0d\u80fd\u7b80\u5355\u6982\u62ec\u4e3a\u201c\u4efb\u4f55\u573a\u5408\u90fd\u4e0d\u8bb8\u540c\u65f6\u6d89\u53ca\u901f\u5ea6\u548c\u538b\u529b\u201d\u3002\u771f\u5b9e\u6848\u4f8b\u5e94\u53c2\u8003\u9501\u5b9a\u7248\u672c\u7684\u5b8c\u6574\u6559\u7a0b\u3002Foundation v13\u8fb9\u754c\u6761\u4ef6\u8bf4\u660e<\/p>\n \u4e94\u3001\u4e0a\u4e0b\u58c1\u9762\u4e0e\u4e8c\u7ef4empty\u8fb9\u754c，\u8981\u5206\u6e05\u4f4d\u7f6e<\/h3>\n![\"\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261020175642-6ad7ab5acd21c.png\") <\/p>\n
\u56fe\u4e2d\u7684\u4e0a\u4e0b\u8fb9\u754c\u662f\u7269\u7406\u58c1\u9762，\u9759\u6b62\u65e0\u6ed1\u79fb：<\/p>\n \\\\[ \\\\boldsymbol U=\\\\boldsymbol 0. \\\\]<\/p>\n \u5c55\u5411\u7684\u524d\u3001\u540e\u4e24\u9762\u7528\u4e8e\u4e8c\u7ef4\u7ea6\u675f，\u4e0d\u662f\u4e0a\u4e0b\u58c1\u9762\u3002<\/p>\n OpenFOAM\u7f51\u683c\u4ecd\u7136\u5177\u6709\u4e09\u7ef4\u4f53\u79ef\u3002\u5e38\u89c1\u4e8c\u7ef4\u8bbe\u7f6e\u91c7\u7528\u5c55\u5411\u5355\u5c42\u5355\u5143，\u5e76\u5c06\u8be5\u65b9\u5411\u4e24\u9762\u8bbe\u7f6e\u4e3aempty，\u76f8\u5e94\u573a\u6587\u4ef6\u4e5f\u9700\u8981\u5339\u914d\u3002\u4e0d\u80fd\u76f4\u63a5\u628a\u539a\u5ea6\u8bbe\u6210\u96f6，\u5236\u9020\u9000\u5316\u5355\u5143\u3002Foundation v13\u7f51\u683c\u5b9a\u4e49\u8bf4\u660e<\/p>\n \u8fd9\u91cc\u8981\u533a\u5206\u4e09\u4ef6\u4e8b：<\/p>\n \n- \u7f51\u683c\u4e2d\u7684walls\u662f\u8fb9\u754c\u540d\u79f0；<\/li>\n
- \u7f51\u683c\u7684type wall\u63cf\u8ff0\u8fb9\u754c\u7c7b\u578b；<\/li>\n
- \u901f\u5ea6\u573a\u4e2d\u7684noSlip\u8868\u8fbe\u672c\u4f8b\u9759\u6b62\u58c1\u9762\u7684\u65e0\u6ed1\u79fb\u6761\u4ef6\u3002<\/li>\n<\/ul>\n
\u7ed9\u8fb9\u754c\u8d77\u540d\u53ebwalls，\u4e0d\u4f1a\u81ea\u52a8\u66ff\u4f60\u8865\u9f50\u6240\u6709\u7269\u7406\u6761\u4ef6\u3002<\/p>\n \u4e0b\u9762\u4ec5\u662f0\/U\u4e2d\u7684\u9605\u8bfb\u7247\u6bb5，\u4e0d\u662f\u5b8c\u6574\u6587\u4ef6，\u4e5f\u4e0d\u662f\u7ec8\u7aef\u547d\u4ee4：<\/p>\n walls
\n{
\n type noSlip;
\n}<\/p>\n frontAndBack
\n{
\n type empty;
\n} <\/p>\n \u5165\u53e3\u3001\u51fa\u53e3\u3001\u6587\u4ef6\u5934\u90e8\u7b49\u5185\u5bb9\u5c1a\u672a\u5305\u542b\u3002<\/p>\n \u53e6\u5916，zeroGradient\u8868\u793a\u6cd5\u5411\u68af\u5ea6\u4e3a\u96f6，\u4e0d\u8868\u793a\u53d8\u91cf\u503c\u4e3a\u96f6\u3002\u57fa\u672c\u8fb9\u754c\u6761\u4ef6\u5b9a\u4e49<\/p>\n \u516d\u3001\u9605\u8bfb\u4e00\u4efd\u4e8c\u7ef4\u7f51\u683c\u6a21\u677f<\/h3>\n\u672c\u8282\u6750\u6599\u63d0\u4f9b\u4e86\u4e00\u4e2a\u7f51\u683c\u5de5\u5177\u793a\u4f8b：<\/p>\n mesh_demo\/
\n README.md
\n system\/
\n blockMeshDict
\n controlDict <\/p>\n \u53c2\u8003\u683c\u5f0f\u4e3aFoundation v13\u3002\u51e0\u4f55\u5c3a\u5bf8\u4e3a：<\/p>\n \\\\[ 1\\\\ \\\\mathrm m \\\\times 0.01\\\\ \\\\mathrm m \\\\times 0.001\\\\ \\\\mathrm m. \\\\]<\/p>\n \u5206\u5757\u6570\u4e3a：<\/p>\n \\\\[ 1000\\\\times20\\\\times1. \\\\]<\/p>\n \u6838\u5fc3\u5b9a\u4e49\u5982\u4e0b：<\/p>\n hex (0 1 2 3 4 5 6 7) (1000 20 1) simpleGrading (1 1 1) <\/p>\n \u6309\u5b57\u5178\u63a8\u7b97：<\/p>\n \\\\[ N_{\\\\mathrm{cells}} = 1000\\\\times20\\\\times1 = 20000, \\\\]\\\\[ \\\\Delta x=0.001\\\\ \\\\mathrm m, \\\\qquad \\\\Delta y=0.0005\\\\ \\\\mathrm m. \\\\]<\/p>\n \u8fd9\u4e9b\u662f\u8bbe\u8ba1\u63a8\u7b97，\u4e0d\u662f\u5df2\u7ecf\u6267\u884c\u7684OpenFOAM\u65e5\u5fd7\u3002<\/p>\n \u5982\u679c\u5df2\u7ecf\u6709\u76f8\u5e94OpenFOAM\u7684Linux\u6216WSL\u73af\u5883，\u53ef\u4ee5\u5148\u590d\u5236\u6a21\u677f\u5230\u81ea\u5df1\u7684\u65b0\u76ee\u5f55，\u518d\u5728\u8be5\u76ee\u5f55\u6267\u884c：<\/p>\n blockMesh
\ncheckMesh <\/p>\n \u6267\u884c\u540e\u5e94\u6838\u67e5\u5b9e\u9645\u5355\u5143\u6570\u3001\u8fb9\u754c\u3001\u7ef4\u6570\u3001\u4f53\u79ef\u548c\u8d28\u91cf，\u5e76\u4fdd\u5b58\u771f\u5b9e\u65e5\u5fd7\u3002\u672c\u6750\u6599\u6ca1\u6709\u6267\u884c\u8fd9\u4e24\u6761\u547d\u4ee4，\u56e0\u6b64\u4e0d\u63d0\u4f9b\u4f2a\u9020\u7684\u6210\u529f\u8f93\u51fa\u3002<\/p>\n \u8be5\u76ee\u5f55\u6ca1\u6709\u5b8c\u6574\u7684\u901f\u5ea6\u3001\u538b\u529b\u3001\u7269\u6027\u548c\u6570\u503c\u914d\u7f6e，\u4e0d\u80fd\u76f4\u63a5\u542f\u52a8\u6d41\u52a8\u6c42\u89e3\u3002\u6a21\u677f\u4e2dcontrolDict\u7684deltaT=1\u4ec5\u4f9b\u7f51\u683c\u5de5\u5177\u6570\u636e\u5e93\u521d\u59cb\u5316，\u4e0d\u662f\u63a8\u8350\u7684CFD\u65f6\u95f4\u6b65\u3002<\/p>\n \u6bd4\u8f83\u6d41\u91cf\u65f6，\u8fd8\u8981\u8003\u8651\u8ba1\u7b97\u539a\u5ea6<\/h4>\n\u672c\u6a21\u677f\u7684\u5c55\u5411\u539a\u5ea6\u4e3a：<\/p>\n \\\\[ T=0.001\\\\ \\\\mathrm m. \\\\]<\/p>\n \u5982\u679c\u540e\u5904\u7406\u8f93\u51fa\u6574\u4e2a\u8ba1\u7b97\u51fa\u53e3\u7684\u4f53\u79ef\u6d41\u91cf，\u5219\u53c2\u8003\u503c\u5e94\u4e3a：<\/p>\n \\\\[ Q_{\\\\mathrm{ref}} = q_{\\\\mathrm{ref}}T \\\\approx 1.666667\\\\times10^{-7}\\\\ \\\\mathrm{m^3\/s}. \\\\]<\/p>\n \u8981\u4e0e\u5355\u4f4d\u5bbd\u5ea6\u6d41\u91cf\u6bd4\u8f83，\u5e94\u518d\u9664\u4ee5\\\\(T\\\\)\u3002<\/p>\n \u4e0d\u80fd\u628a\\\\(\\\\mathrm{m^3\/s}\\\\)\u76f4\u63a5\u4e0e\u4e0a\u4e00\u8282\u7684\\\\(\\\\mathrm{m^2\/s}\\\\)\u6570\u503c\u6bd4\u8f83，\u4e5f\u4e0d\u80fd\u6df7\u5165\u8d28\u91cf\u6d41\u91cf\\\\(\\\\mathrm{kg\/s}\\\\)\u3002<\/p>\n \u4e03\u3001\u5148\u505a\u4e00\u4e2a\u53ef\u4ee5\u624b\u7b97\u7684\u79ef\u5206\u8bef\u5dee\u5b9e\u9a8c<\/h3>\n\u628a\u4e0a\u4e00\u8282\u89e3\u6790\u901f\u5ea6\u5256\u9762\u5206\u6210\\\\(N\\\\)\u4e2a\u533a\u95f4：<\/p>\n \\\\[ \\\\Delta y=\\\\frac HN. \\\\]<\/p>\n \u7528\u590d\u5408\u68af\u5f62\u516c\u5f0f\u8ba1\u7b97\u5355\u4f4d\u5bbd\u5ea6\u6d41\u91cf：<\/p>\n \\\\[ q_N = \\\\sum_{i=0}^{N-1} \\\\frac{u_i+u_{i+1}}2\\\\,\\\\Delta y. \\\\]<\/p>\n \u5b9a\u4e49\u76f8\u5bf9\u8bef\u5dee：<\/p>\n \\\\[ e_q = \\\\left| \\\\frac{q_N}{q_{\\\\mathrm{ref}}}-1 \\\\right|. \\\\]<\/p>\n \u8ba1\u7b97\u7ed3\u679c\u4e3a：<\/p>\n \n\u5206\u6bb5\u6570 \\\\(N\\\\)\\\\(\\\\Delta y\\\\)\/m\u79ef\u5206\u76f8\u5bf9\u8bef\u5dee<\/tr>\n \n\n| 10<\/td>\n | 0.001<\/td>\n | 1.000000%<\/td>\n<\/tr>\n | \n| 20<\/td>\n | 0.0005<\/td>\n | 0.250000%<\/td>\n<\/tr>\n | \n| 40<\/td>\n | 0.00025<\/td>\n | 0.062500%<\/td>\n<\/tr>\n | \n| 80<\/td>\n | 0.000125<\/td>\n | 0.015625%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \u5bf9\u8fd9\u6761\u5747\u5300\u91c7\u6837\u7684\u629b\u7269\u7ebf：<\/p>\n \\\\[ e_q=\\\\frac1{N^2}. \\\\]<\/p>\n \u6240\u4ee5，\u5206\u6bb5\u6570\u7ffb\u500d，\u8bef\u5dee\u7ea6\u7f29\u5c0f\u56db\u500d\u3002<\/p>\n \u7531\u5df2\u77e5\u8bef\u5dee\u53ef\u4ee5\u4f30\u8ba1\u89c2\u5bdf\u9636\u6570：<\/p>\n \\\\[ p= \\\\frac{\\\\ln(e_N\/e_{2N})}{\\\\ln2} \\\\approx2. \\\\]<\/p>\n \u4f46\u8fd9\u53ea\u662f\u672c\u79ef\u5206\u7ec3\u4e60\u7684\u89c2\u5bdf\u9636\u6570\u3002<\/p>\n \u6240\u6709\u901f\u5ea6\u503c\u90fd\u6765\u81ea\u89e3\u6790\u516c\u5f0f，\u7a0b\u5e8f\u6ca1\u6709\u5728\u4e0d\u540c\u7f51\u683c\u4e0a\u91cd\u65b0\u6c42\u89e3Navier\u2013Stokes\u65b9\u7a0b\u3002\u56e0\u6b64：<\/p>\n \\\\[ \\\\text{\u89e3\u6790\u51fd\u6570\u79ef\u5206\u8bef\u5dee\u4e0b\u964d} \\\\neq \\\\text{\u771f\u5b9eCFD\u7f51\u683c\u6536\u655b}. \\\\]<\/p>\n \u771f\u5b9eCFD\u8bef\u5dee\u8fd8\u53ef\u80fd\u6765\u81ea\u7a7a\u95f4\u79bb\u6563\u3001\u8fb9\u754c\u3001\u8fed\u4ee3\u3001\u65f6\u95f4\u63a8\u8fdb\u548c\u540e\u5904\u7406，\u4e0d\u80fd\u7528\u8fd9\u5f20\u8868\u8bc1\u660e\u67d0\u4e2aOpenFOAM\u6a21\u578b\u5df2\u7ecf\u4e8c\u9636\u6536\u655b\u3002<\/p>\n \u516b\u3001\u65f6\u95f4\u6b65：\u4e00\u6b65\u4e4b\u5185，\u6d41\u52a8\u8de8\u8fc7\u591a\u5c11\u5355\u5143？<\/h3>\n\u4e00\u7ef4\u76f4\u89c2\u4f30\u8ba1\u4e3a：<\/p>\n \\\\[ Co\\\\approx\\\\frac{|U|\\\\Delta t}{\\\\Delta x}. \\\\]<\/p>\n \u5b83\u79f0\u4e3aCourant\u6570\u3002<\/p>\n \u5148\u7528\u4e00\u4e2a\u72ec\u7acb\u6559\u5b66\u901f\u5ea6：<\/p>\n \\\\[ U=0.1\\\\ \\\\mathrm{m\/s}. \\\\]<\/p>\n \u8fd9\u4e0d\u662f\u4e0a\u4e00\u8282\u57fa\u51c6\u7684\u6700\u5927\u901f\u5ea6\u3002<\/p>\n \u53d6：<\/p>\n \\\\[ \\\\Delta x=0.001\\\\ \\\\mathrm m, \\\\qquad \\\\Delta t=0.002\\\\ \\\\mathrm s. \\\\]<\/p>\n \u5f97\u5230：<\/p>\n \\\\[ Co = \\\\frac{0.1\\\\times0.002}{0.001} = 0.2. \\\\]<\/p>\n \u5982\u679c\u8bfe\u5802\u6682\u9009\u76ee\u6807：<\/p>\n \\\\[ Co\\\\le0.5, \\\\]<\/p>\n \u5219\u4f30\u7b97：<\/p>\n \\\\[ \\\\Delta t \\\\le \\\\frac{0.5\\\\Delta x}{|U|} = 0.005\\\\ \\\\mathrm s. \\\\]<\/p>\n \u8fd9\u91cc\u76840.5\u53ea\u662f\u793a\u4f8b\u76ee\u6807，\u4e0d\u662f\u6240\u6709\u683c\u5f0f\u548c\u6c42\u89e3\u5668\u7684\u901a\u7528\u7a33\u5b9a\u6761\u4ef6\u3002<\/p>\n \u7f51\u683c\u52a0\u5bc6\u540e，\u539f\u65f6\u95f4\u6b65\u672a\u5fc5\u8fd8\u5408\u9002<\/h4>\n\n\u60c5\u51b5\\\\(\\\\Delta x\\\\)\/m\\\\(\\\\Delta t\\\\)\/s\\\\(Co\\\\)\u4f30\u7b97<\/tr>\n \n\n| \u539f\u8bbe\u7f6e<\/td>\n | 0.001<\/td>\n | 0.002<\/td>\n | 0.2<\/td>\n<\/tr>\n | \n| \u53ea\u628a\u95f4\u8ddd\u51cf\u534a<\/td>\n | 0.0005<\/td>\n | 0.002<\/td>\n | 0.4<\/td>\n<\/tr>\n | \n| \u95f4\u8ddd\u4e0e\u65f6\u95f4\u6b65\u5747\u51cf\u534a<\/td>\n | 0.0005<\/td>\n | 0.001<\/td>\n | 0.2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \u7a7a\u95f4\u548c\u65f6\u95f4\u8bbe\u7f6e\u76f8\u4e92\u5f71\u54cd\u3002<\/p>\n \u4f46\u51cf\u5c0f\u65f6\u95f4\u6b65，\u4e0d\u80fd\u4fee\u590d\u9519\u8bef\u58c1\u9762\u6761\u4ef6，\u4e5f\u4e0d\u80fd\u4fee\u590d\u65e0\u6548\u7f51\u683c\u3002<\/p>\n \u4e5d\u3001\u5b9e\u9645Co\u4e0d\u80fd\u53ea\u9760\u4e00\u4e2a\u5168\u5c40\u901f\u5ea6\u4ee3\u66ff<\/h3>\n\u5bf9\u4e8e\u4f7f\u7528\u4f53\u79ef\u9762\u901a\u91cf\u7684\u5e38\u89c1\u5b9a\u4e49：<\/p>\n \\\\[ Co = \\\\frac{\\\\Delta t}{2V} \\\\sum_f|\\\\phi_f|. \\\\]<\/p>\n \u5176\u4e2d：<\/p>\n \n- \\\\(V\\\\)：\u5355\u5143\u4f53\u79ef；<\/li>\n
- \\\\(\\\\phi_f\\\\)：\u9762\u4f53\u79ef\u901a\u91cf；<\/li>\n
- \\\\(f\\\\)：\u5355\u5143\u5404\u4e2a\u9762\u3002<\/li>\n<\/ul>\n
\u8fd9\u4e2a\u5b9a\u4e49\u8003\u8651\u5c40\u90e8\u7f51\u683c\u548c\u901a\u91cf，\u6bd4\u5355\u4e2a\\\\(U\\\\Delta t\/\\\\Delta x\\\\)\u5305\u542b\u66f4\u591a\u4fe1\u606f\u3002OpenFOAM Courant\u6570\u8bf4\u660e<\/p>\n \u5b9e\u9645\u8ba1\u7b97\u5e94\u68c0\u67e5\u5c40\u90e8\u548c\u6700\u5927Co，\u4e0d\u80fd\u4ec5\u770b\u5e73\u5747\u901f\u5ea6，\u4e5f\u4e0d\u80fd\u673a\u68b0\u5730\u7528\u4e00\u4e2a\u6700\u5c0f\u8fb9\u957f\u4ee3\u66ff\u5b8c\u6574\u7684\u901a\u91cf\u8ba1\u7b97\u3002<\/p>\n \u8fd8\u8981\u533a\u5206：<\/p>\n \n- \u6570\u503c\u7a33\u5b9a；<\/li>\n
- \u65f6\u95f4\u8bef\u5dee\u8db3\u591f\u5c0f；<\/li>\n
- \u975e\u7ebf\u6027\u8fed\u4ee3\u5145\u5206；<\/li>\n
- \u6700\u7ec8\u7269\u7406\u7ed3\u679c\u6b63\u786e\u3002<\/li>\n<\/ul>\n
\u5b83\u4eec\u4e0d\u662f\u540c\u4e00\u4ef6\u4e8b\u3002<\/p>\n \u9690\u5f0f\u683c\u5f0f\u4e5f\u9700\u8981\u65f6\u95f4\u7cbe\u5ea6\u68c0\u67e5；\u7a33\u6001\u8fed\u4ee3\u6b21\u6570\u4e5f\u4e0d\u80fd\u4e00\u6982\u5f53\u6210\u771f\u5b9e\u7269\u7406\u65f6\u95f4\u6b65\u3002<\/p>\n \u56de\u5230\u4e0a\u4e00\u8282：<\/p>\n \\\\[ u_{\\\\max}=0.025\\\\ \\\\mathrm{m\/s}. \\\\]<\/p>\n \u91c7\u7528\u76f8\u540c\u95f4\u8ddd\u548c\u65f6\u95f4\u6b65，\u4e00\u7ef4\u4f30\u7b97\u4e3a：<\/p>\n \\\\[ Co_{\\\\mathrm{estimate}} = \\\\frac{0.025\\\\times0.002}{0.001} = 0.05. \\\\]<\/p>\n \u5728\u8bfe\u5802\u76ee\u68070.5\u4e0b，\u65f6\u95f4\u6b65\u4e0a\u9650\u4f30\u7b97\u4e3a0.02 s\u3002<\/p>\n \u8fd9\u4ecd\u7136\u662f\u4f30\u7b97，\u4e0d\u662f\u67d0\u4e2a\u672a\u6267\u884cOpenFOAM\u6848\u4f8b\u7684\u5b9e\u6d4b\u6700\u5927Co\u3002<\/p>\n \u5341\u3001\u8fd0\u884c\u5b8c\u6574Python\u7ec3\u4e60<\/h3>\n\u8bf7\u5c06\u4e24\u4e2a\u6587\u4ef6\u653e\u5728\u540c\u4e00\u76ee\u5f55：<\/p>\n lesson56_settings.py：<\/p>\n """Analytical-profile quadrature and scalar Courant estimates, not a CFD solver."""
\nimport argparse
\nimport csv
\nimport json
\nimport math
\nfrom pathlib import Path<\/p>\n from lesson55_channel import channel_profile<\/p>\n def quadrature_study():
\n rows = []
\n for n in (10, 20, 40, 80):
\n summary, profile, _ = channel_profile(n=n)
\n dy = summary['parameters']['H_m']\/n
\n q = math.fsum((a['u_x_m_per_s']+b['u_x_m_per_s'])*dy\/2
\n for a, b in zip(profile[:-1], profile[1:]))
\n exact = summary['q_per_width_m2_per_s']
\n error = abs(q\/exact-1)
\n order = math.log(rows[-1]['relative_error']\/error)\/math.log(2) if rows else None
\n rows.append({'N': n, 'dy_m': dy, 'q_trap_m2_per_s': q,
\n 'q_exact_m2_per_s': exact, 'relative_error': error,
\n 'observed_quadrature_order': order})
\n return rows<\/p>\n def courant_estimate(speed, dx, dt, target=.5):
\n for name, value in (('speed', speed), ('dx', dx), ('dt', dt), ('target', target)):
\n if (isinstance(value, bool) or not isinstance(value, (int,float))
\n or not math.isfinite(value) or value <= 0):
\n raise ValueError(name+' must be a finite positive number')
\n co, limit = speed*dt\/dx, target*dx\/speed
\n if not math.isfinite(co) or not math.isfinite(limit) or limit <= 0:
\n raise ValueError('derived Courant values invalid')
\n return {'speed_m_per_s': speed, 'dx_m': dx, 'dt_s': dt,
\n 'Co_estimate': co, 'target_Co': target, 'dt_limit_s': limit}<\/p>\n def self_test():
\n rows = quadrature_study()
\n assert len(rows) == 4
\n for row in rows:
\n assert math.isclose(row['relative_error'], 1\/row['N']**2, rel_tol=1e-9)
\n assert math.isclose(row['q_exact_m2_per_s'], 1\/6000)
\n assert all(math.isclose(r['observed_quadrature_order'],2,abs_tol=1e-9) for r in rows[1:])
\n base = courant_estimate(.1,.001,.002)
\n assert math.isclose(base['Co_estimate'],.2) and math.isclose(base['dt_limit_s'],.005)
\n fine = courant_estimate(.1,.0005,.002)
\n assert math.isclose(fine['Co_estimate'],.4)
\n assert math.isclose(courant_estimate(.1,.0005,.001)['Co_estimate'],.2)
\n assert math.isclose(courant_estimate(.025,.001,.002)['Co_estimate'],.05)
\n for args in ((0,.001,.002),(.1,0,.002),(.1,.001,float('nan'))):
\n try:
\n courant_estimate(*args)
\n except ValueError:
\n pass
\n else:
\n raise AssertionError('invalid input accepted')
\n print('SELF_TEST_OK')<\/p>\n def write_csv(path, rows):
\n with path.open('x',newline='',encoding='utf-8-sig') as handle:
\n writer = csv.DictWriter(handle,fieldnames=list(rows[0]))
\n writer.writeheader()
\n writer.writerows(rows)<\/p>\n def main():
\n parser = argparse.ArgumentParser(description=__doc__)
\n parser.add_argument('–speed',type=float,default=.1,help='positive advection speed, m\/s')
\n parser.add_argument('–dx',type=float,default=.001,help='streamwise spacing, m')
\n parser.add_argument('–dt',type=float,default=.002,help='time step, s')
\n parser.add_argument('–co-target',type=float,default=.5,help='classroom target, not a universal rule')
\n parser.add_argument('–out',type=Path,help='new output directory only')
\n parser.add_argument('–self-test',action='store_true')
\n args = parser.parse_args()
\n if args.self_test:
\n self_test()
\n return 0
\n try:
\n rows = quadrature_study()
\n base = courant_estimate(args.speed,args.dx,args.dt,args.co_target)
\n cases = [dict(case='base',**base),
\n dict(case='half_dx_same_dt',**courant_estimate(args.speed,args.dx\/2,args.dt,args.co_target)),
\n dict(case='half_dx_half_dt',**courant_estimate(args.speed,args.dx\/2,args.dt\/2,args.co_target))]
\n summary = {'mode':'ANALYTICAL_QUADRATURE_AND_SCALAR_COURANT_ESTIMATE',
\n 'OpenFOAM_run':False, 'quadrature_source':'lesson55_channel.channel_profile',
\n 'quadrature_is_CFD_mesh_convergence':False,
\n 'courant_base':base, 'max_observed_quadrature_order':max(r['observed_quadrature_order'] for r in rows[1:])}
\n if args.out:
\n args.out.mkdir(parents=True,exist_ok=False)
\n write_csv(args.out\/'quadrature.csv',rows)
\n write_csv(args.out\/'courant_cases.csv',cases)
\n (args.out\/'summary.json').write_text(json.dumps(summary,indent=2,allow_nan=False),encoding='utf-8')
\n for row in rows:
\n print(f'N={row["N"]}; integration_error={100*row["relative_error"]:.6f}%')
\n print(f'observed_quadrature_order={summary["max_observed_quadrature_order"]:.6f}')
\n print(f'Co={base["Co_estimate"]:.3f}; dt_limit={base["dt_limit_s"]:.6f} s')
\n print('MODE=QUADRATURE_AND_COURANT_ESTIMATE; OpenFOAM_NOT_RUN')
\n return 0
\n except (OSError,ValueError,ArithmeticError) as exc:
\n print('INPUT_OR_OUTPUT_ERROR: '+str(exc))
\n return 2<\/p>\n if __name__ == '__main__':
\n raise SystemExit(main())<\/p>\n lesson55_channel.py：<\/p>\n """Analytical plane Poiseuille benchmark. No CFD equations are discretised or solved."""
\nimport argparse
\nimport csv
\nimport json
\nimport math
\nfrom pathlib import Path<\/p>\n def channel_profile(mu=0.001, gradient=2.0, n=20):
\n for name, value in (('mu', mu), ('gradient', gradient)):
\n if (isinstance(value, bool) or not isinstance(value, (int, float))
\n or not math.isfinite(value) or value <= 0):
\n raise ValueError(name + ' must be a finite positive number')
\n if type(n) is not int or not 2 <= n <= 10000:
\n raise ValueError('n must be an integer in [2, 10000]')
\n H, L, rho = 0.01, 1.0, 1000.0
\n nu = mu\/rho
\n y = [H*i\/n for i in range(n+1)]
\n u = [gradient*v*(H-v)\/(2*mu) for v in y]
\n q = gradient*H**3\/(12*mu)
\n mean, maximum = q\/H, gradient*H**2\/(8*mu)
\n summary = {'source': 'ANALYTICAL_PLANE_POISEUILLE', 'OpenFOAM_run': False,
\n 'parameters': {'H_m': H, 'L_m': L, 'rho_kg_per_m3': rho,
\n 'mu_Pa_s': mu, 'G_Pa_per_m': gradient},
\n 'nu_m2_per_s': nu, 'U_mean_m_per_s': mean, 'U_max_m_per_s': maximum,
\n 'q_per_width_m2_per_s': q, 'Re_Dh': mean*(2*H)\/nu,
\n 'delta_p_static_Pa': gradient*L,
\n 'delta_p_kinematic_m2_per_s2': gradient*L\/rho}
\n numeric = [nu, mean, maximum, q, summary['Re_Dh'], summary['delta_p_static_Pa'],
\n summary['delta_p_kinematic_m2_per_s2']] + u
\n if not all(math.isfinite(v) for v in numeric) or min(nu, mean, maximum, q) <= 0:
\n raise ValueError('derived values are not finite and positive')
\n checks = {'no_slip': u[0] == 0 and u[-1] == 0,
\n 'symmetry': all(math.isclose(a, b, rel_tol=1e-12, abs_tol=1e-15)
\n for a, b in zip(u, reversed(u))),
\n 'peak_to_mean': math.isclose(maximum\/mean, 1.5, rel_tol=1e-12)}
\n if not all(checks.values()):
\n raise ValueError('analytical consistency checks failed')
\n summary['analytical_checks'] = checks
\n summary['profile_points'] = n+1
\n profile = [{'y_m': v, 'u_x_m_per_s': speed} for v, speed in zip(y, u)]
\n pressure = [{'x_m': L*i\/4, 'p_static_Pa': gradient*(L-L*i\/4),
\n 'p_kinematic_m2_per_s2': gradient*(L-L*i\/4)\/rho} for i in range(5)]
\n return summary, profile, pressure<\/p>\n def self_test():
\n base, rows, pressure = channel_profile()
\n assert len(rows) == 21 and len(pressure) == 5
\n assert math.isclose(base['U_mean_m_per_s'], 1\/60)
\n assert math.isclose(base['U_max_m_per_s'], .025)
\n assert math.isclose(base['q_per_width_m2_per_s'], 1\/6000)
\n assert math.isclose(base['Re_Dh'], 1000\/3)
\n assert math.isclose(pressure[0]['p_kinematic_m2_per_s2'], .002)
\n doubled, _, _ = channel_profile(gradient=4)
\n viscous, _, _ = channel_profile(mu=.002)
\n assert math.isclose(doubled['U_mean_m_per_s']\/base['U_mean_m_per_s'], 2)
\n assert math.isclose(viscous['U_mean_m_per_s']\/base['U_mean_m_per_s'], .5)
\n assert math.isclose(viscous['Re_Dh']\/base['Re_Dh'], .25)
\n for kwargs in ({'mu': 0}, {'mu': -1}, {'gradient': float('nan')}, {'n': 0}):
\n try:
\n channel_profile(**kwargs)
\n except ValueError:
\n pass
\n else:
\n raise AssertionError('invalid input accepted')
\n print('SELF_TEST_OK')<\/p>\n def main():
\n parser = argparse.ArgumentParser(description=__doc__)
\n parser.add_argument('–mu', type=float, default=.001, help='dynamic viscosity, Pa s')
\n parser.add_argument('–gradient', type=float, default=2, help='G=-dp_static\/dx, Pa\/m')
\n parser.add_argument('–out', type=Path, help='new output directory; existing directory rejected')
\n parser.add_argument('–self-test', action='store_true')
\n args = parser.parse_args()
\n if args.self_test:
\n self_test()
\n return 0
\n try:
\n summary, profile, pressure = channel_profile(mu=args.mu, gradient=args.gradient)
\n if args.out:
\n args.out.mkdir(parents=True, exist_ok=False)
\n (args.out\/'summary.json').write_text(json.dumps(summary, indent=2, allow_nan=False), encoding='utf-8')
\n for name, rows in (('profile.csv', profile), ('pressure.csv', pressure)):
\n with (args.out\/name).open('x', newline='', encoding='utf-8-sig') as handle:
\n writer = csv.DictWriter(handle, fieldnames=list(rows[0]))
\n writer.writeheader()
\n writer.writerows(rows)
\n print('MODE=ANALYTICAL; OpenFOAM_NOT_RUN')
\n print(f'nu={summary["nu_m2_per_s"]:.9e} m2\/s')
\n print(f'U_mean={summary["U_mean_m_per_s"]:.6f} m\/s; U_max={summary["U_max_m_per_s"]:.6f} m\/s')
\n print(f'q_per_width={summary["q_per_width_m2_per_s"]:.9f} m2\/s; Re_Dh={summary["Re_Dh"]:.3f}')
\n print(f'delta_p_static={summary["delta_p_static_Pa"]:.6f} Pa; delta_p_kinematic={summary["delta_p_kinematic_m2_per_s2"]:.9f} m2\/s2')
\n print('ANALYTICAL_CHECKS=PASS')
\n return 0
\n except (OSError, ValueError, ArithmeticError) as exc:
\n print('INPUT_OR_OUTPUT_ERROR: ' + str(exc))
\n return 2<\/p>\n if __name__ == '__main__':
\n raise SystemExit(main())<\/p>\n \u4e3b\u7a0b\u5e8f\u53ea\u4f7f\u7528Python\u6807\u51c6\u5e93\u3002<\/p>\n 10.1 \u6267\u884c\u81ea\u68c0<\/h4>\npython lesson56_settings.py –self-test <\/p>\n \u9884\u671f\u8f93\u51fa：<\/p>\n SELF_TEST_OK <\/p>\n 10.2 \u8fd0\u884c\u7ec3\u4e60<\/h4>\npython lesson56_settings.py <\/p>\n \u5b9e\u6d4b\u8f93\u51fa：<\/p>\n N=10; integration_error=1.000000%
\nN=20; integration_error=0.250000%
\nN=40; integration_error=0.062500%
\nN=80; integration_error=0.015625%
\nobserved_quadrature_order=2.000000
\nCo=0.200; dt_limit=0.005000 s
\nMODE=QUADRATURE_AND_COURANT_ESTIMATE; OpenFOAM_NOT_RUN <\/p>\n \u5176\u4e2d：<\/p>\n \n- \u79ef\u5206\u4f7f\u7528\u4e0a\u4e00\u8282\u7684\u7269\u7406\u57fa\u51c6；<\/li>\n
- Co\u9ed8\u8ba4\u901f\u5ea6\u91c7\u7528\u72ec\u7acb\u6559\u5b66\u503c0.1 m\/s；<\/li>\n
- \u8f93\u51fa\u660e\u786e\u6807\u6ce8\u672a\u8fd0\u884cOpenFOAM\u3002<\/li>\n<\/ul>\n
10.3 \u4fdd\u5b58\u6570\u636e<\/h4>\npython lesson56_settings.py –out run56_01 <\/p>\n \u63a7\u5236\u53f0\u6570\u503c\u4e0d\u53d8，\u540c\u65f6\u751f\u6210：<\/p>\n run56_01\/
\n quadrature.csv
\n courant_cases.csv
\n summary.json <\/p>\n \u8bfe\u7a0b\u5305\u5df2\u7ecf\u5305\u542breference_run\u6837\u672c\u3002\u91cd\u65b0\u8fd0\u884c\u65f6\u8bf7\u4f7f\u7528\u65b0\u76ee\u5f55，\u5df2\u6709\u8f93\u51fa\u76ee\u5f55\u4e0d\u4f1a\u88ab\u8986\u76d6\u3002<\/p>\n 10.4 \u4f7f\u7528\u4e0a\u4e00\u8282\u6700\u5927\u901f\u5ea6<\/h4>\npython lesson56_settings.py –speed 0.025 <\/p>\n \u5173\u952e\u8f93\u51fa：<\/p>\n Co=0.050; dt_limit=0.020000 s <\/p>\n 10.5 \u53ea\u628a\u6d41\u5411\u95f4\u8ddd\u51cf\u534a<\/h4>\npython lesson56_settings.py –dx 0.0005 <\/p>\n \u5173\u952e\u8f93\u51fa：<\/p>\n Co=0.400; dt_limit=0.002500 s <\/p>\n \u8fd9\u4e24\u6761\u547d\u4ee4\u4ecd\u4f1a\u6253\u5370\u76f8\u540c\u7684\u79ef\u5206\u8bef\u5dee\u8868，\u56e0\u4e3a\u5b83\u4eec\u53ea\u6539\u53d8Co\u4f30\u7b97\u8f93\u5165\u3002<\/p>\n \u5341\u4e00\u3001\u67e5\u770b\u5b9e\u9645\u7ed3\u679c\u56fe<\/h3>\n![\"\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261020175643-6ad7ab5ba1565.png\") <\/p>\n
\u5de6\u56fe\u5c55\u793a\u89e3\u6790\u901f\u5ea6\u91c7\u6837\u7684\u68af\u5f62\u79ef\u5206\u8bef\u5dee\u3002<\/p>\n \u53f3\u56fe\u5c55\u793a\u6559\u5b66\u901f\u5ea60.1 m\/s\u4e0b，\u95f4\u8ddd\u548c\u65f6\u95f4\u6b65\u53d8\u5316\u5bf9Co\u4f30\u7b97\u7684\u5f71\u54cd\u3002<\/p>\n \u7ea2\u8272\u865a\u7ebf\u662f\u8bfe\u5802\u793a\u4f8b\u76ee\u6807，\u4e0d\u662f\u666e\u904d\u5b89\u5168\u7ebf\u3002<\/p>\n \u9700\u8981\u91cd\u65b0\u751f\u6210\u4e24\u5f20\u914d\u56fe\u65f6，\u5c06plot_lesson56.py\u4e0e\u65f6\u95f4\u6b65plot_lesson56.py\u653e\u5728\u540c\u4e00\u76ee\u5f55，\u5728\u5b89\u88c5\u4e86Matplotlib\u7684\u73af\u5883\u8fd0\u884c：<\/p>\n python plot_lesson56.py –data run56_01 –out figures56_01 <\/p>\n \u9884\u671f\u8f93\u51fa：<\/p>\n FIGURES_OK: lesson56_error_and_courant.png, lesson56_boundary_map.png <\/p>\n \u6ca1\u6709Matplotlib\u4e5f\u4e0d\u5f71\u54cd\u4e3b\u7a0b\u5e8f，\u53ef\u4ee5\u76f4\u63a5\u9605\u8bfb\u6750\u6599\u4e2d\u7684\u914d\u56fe\u3002<\/p>\n \u5341\u4e8c\u3001\u600e\u6837\u8bbe\u8ba1\u771f\u6b63\u7684\u7a7a\u95f4\u4e0e\u65f6\u95f4\u7814\u7a76？<\/h3>\n\u4e0b\u9762\u662f\u4e00\u4efd\u7814\u7a76\u8ba1\u5212，\u4e0d\u662f\u5df2\u7ecf\u8ba1\u7b97\u5b8c\u6210\u7684CFD\u7ed3\u679c\u3002<\/p>\n \n\u7f51\u683c\\\\(N_x\\\\times N_y\\\\times N_z\\\\)\u5355\u5143\u6570\\\\(\\\\Delta x\\\\)\/m\\\\(\\\\Delta y\\\\)\/m<\/tr>\n \n\n| G1<\/td>\n | 500\u00d710\u00d71<\/td>\n | 5000<\/td>\n | 0.002<\/td>\n | 0.001<\/td>\n<\/tr>\n | \n| G2<\/td>\n | 1000\u00d720\u00d71<\/td>\n | 20000<\/td>\n | 0.001<\/td>\n | 0.0005<\/td>\n<\/tr>\n | \n| G3<\/td>\n | 2000\u00d740\u00d71<\/td>\n | 80000<\/td>\n | 0.0005<\/td>\n | 0.00025<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \u6bcf\u5f20\u7f51\u683c\u90fd\u9700\u8981\u91cd\u65b0\u6c42\u89e3，\u5e76\u63d0\u53d6\u540c\u4e00\u6307\u6807，\u4f8b\u5982：<\/p>\n \n- \u5355\u4f4d\u5bbd\u5ea6\u6d41\u91cf；<\/li>\n
- \u540c\u4e00\u622a\u9762\u7684\u901f\u5ea6\u5256\u9762\u8bef\u5dee；<\/li>\n
- \u58c1\u9762\u526a\u5e94\u529b\u3002<\/li>\n<\/ul>\n
\u6307\u6807\u8fd8\u8981\u7ed3\u5408\u9a71\u52a8\u65b9\u5f0f\u9009\u62e9\u3002\u5982\u679c\u538b\u529b\u5dee\u672c\u6765\u5c31\u662f\u6307\u5b9a\u7684\u8f93\u5165，\u4ec5\u770b\u5230\u5b83\u5728\u5404\u5de5\u51b5\u76f8\u540c，\u4e0d\u80fd\u8bc1\u660e\u89e3\u5df2\u7ecf\u6536\u655b\u3002<\/p>\n \u7a7a\u95f4\u7814\u7a76<\/h4>\n\u4fdd\u6301\u51e0\u4f55\u3001\u7269\u6027\u3001\u8fb9\u754c\u548c\u63d0\u53d6\u65b9\u5f0f\u4e00\u81f4，\u63a7\u5236\u8fed\u4ee3\u4e0e\u65f6\u95f4\u8bef\u5dee\u3002<\/p>\n \u5982\u679c\u968f\u7f51\u683c\u52a0\u5bc6\u540c\u65f6\u7f29\u5c0f\u65f6\u95f4\u6b65，\u7ed3\u679c\u53d8\u5316\u53ef\u80fd\u6df7\u5408\u4e86\u7a7a\u95f4\u548c\u65f6\u95f4\u5f71\u54cd，\u4e0d\u80fd\u5168\u90e8\u5f52\u56e0\u4e8e\u7f51\u683c\u3002<\/p>\n \u65f6\u95f4\u7814\u7a76<\/h4>\n\u56fa\u5b9a\u7a7a\u95f4\u7f51\u683c，\u6bd4\u8f83\u4e0d\u540c\u65f6\u95f4\u6b65\u5728\u76f8\u540c\u7269\u7406\u65f6\u523b\u7684\u54cd\u5e94\u3002<\/p>\n \u5982\u679c\u8981\u4e0e\u7a33\u6001\u89e3\u6790\u89e3\u6bd4\u8f83，\u8fd8\u5e94\u786e\u8ba4\u5df2\u7ecf\u8fbe\u5230\u7a33\u6001\u3002\u91c7\u7528\u5c0f\u65f6\u95f4\u6b65，\u4e0d\u7b49\u4e8e\u5df2\u7ecf\u5145\u5206\u53d1\u5c55\u6216\u8fbe\u5230\u7a33\u6001\u3002<\/p>\n \u5efa\u8bae\u81f3\u5c11\u7528\u4e09\u7ec4\u6709\u89c4\u5f8b\u7684\u8bbe\u7f6e\u68c0\u67e5\u8d8b\u52bf\u3002\u4f30\u8ba1\u89c2\u5bdf\u9636\u6570\u6216\u5916\u63a8\u8bef\u5dee\u65f6，\u8fd8\u8981\u68c0\u67e5\u52a0\u5bc6\u65b9\u5f0f\u3001\u6e10\u8fd1\u533a\u548c\u7ed3\u679c\u884c\u4e3a，\u4e0d\u80fd\u673a\u68b0\u5957\u7528\u672c\u8282\u79ef\u5206\u5b9e\u9a8c\u7684\u4e8c\u9636\u7ed3\u8bba\u3002<\/p>\n \u5341\u4e09\u3001\u8bfe\u540e\u7ec3\u4e60\u4e0e\u9a8c\u6536<\/h3>\n\u7ec3\u4e60\u4e00：\u7ee7\u7eed\u589e\u52a0\u5206\u6bb5\u6570<\/h4>\n\u5f53：<\/p>\n \\\\[ N=160 \\\\]<\/p>\n \u65f6，\u79ef\u5206\u8bef\u5dee\u9884\u8ba1\u662f\u591a\u5c11？<\/p>\n \u53c2\u8003\u7b54\u6848：<\/p>\n \\\\[ e_q = \\\\frac1{160^2} = 0.00390625\\\\%. \\\\]<\/p>\n \u7ec3\u4e60\u4e8c：\u4fdd\u6301Co\u4e0d\u53d8<\/h4>\n\u56fa\u5b9a\u901f\u5ea6，\u5c06\u6d41\u5411\u95f4\u8ddd\u51cf\u534a，\u65f6\u95f4\u6b65\u5e94\u8be5\u600e\u6837\u53d8\u5316？<\/p>\n \u53c2\u8003\u7b54\u6848：\u5728\u672c\u8282\u4e00\u7ef4\u4f30\u7b97\u4e2d，\u65f6\u95f4\u6b65\u4e5f\u5e94\u51cf\u534a\u3002<\/p>\n \u7ec3\u4e60\u4e09：\u7a33\u5b9a\u7ed3\u679c\u662f\u5426\u4e00\u5b9a\u6b63\u786e？<\/h4>\n\u58c1\u9762\u8bef\u8bbe\u4e3a\u6ed1\u79fb，\u7f51\u683c\u52a0\u5bc6\u540e\u7ed3\u679c\u975e\u5e38\u7a33\u5b9a，\u53ef\u4ee5\u8ba4\u4e3a\u6b63\u786e\u5417？<\/p>\n \u53c2\u8003\u7b54\u6848：\u4e0d\u80fd\u3002\u5b83\u53ef\u80fd\u6536\u655b\u5230\u4e86\u53e6\u4e00\u4e2a\u7269\u7406\u95ee\u9898\u3002<\/p>\n \u7ec3\u4e60\u56db：\u7f51\u683c\u68c0\u67e5\u662f\u5426\u66ff\u4ee3\u8fb9\u754c\u68c0\u67e5？<\/h4>\ncheckMesh\u901a\u8fc7\u4ee5\u540e，\u662f\u5426\u8fd8\u8981\u6838\u5bf9U\u3001p\u7684\u8fb9\u754c\u8bbe\u7f6e？<\/p>\n \u53c2\u8003\u7b54\u6848：\u8981\u3002\u7f51\u683c\u68c0\u67e5\u4e0d\u7b49\u4e8e\u5b8c\u6574\u7684\u7269\u7406\u4e0e\u6570\u503c\u9a8c\u6536\u3002<\/p>\n \u672c\u8282\u4ea4\u4ed8<\/h4>\n\u51c6\u5907\u4e24\u4efd\u8868：<\/p>\n - \u5df2\u8fd0\u884c\u7684\u79ef\u5206\u8bef\u5dee\u8868\u3002<\/li>\n
- \u5c1a\u5f85\u771f\u5b9e\u6c42\u89e3\u7684CFD\u7a7a\u95f4\u2014\u65f6\u95f4\u7814\u7a76\u8ba1\u5212\u3002<\/li>\n
\u80fd\u591f\u533a\u5206\u4ee5\u4e0b\u4e09\u7c7b\u4fe1\u606f，\u4e5f\u662f\u9a8c\u6536\u8981\u6c42：<\/p>\n \u5b9e\u6d4bPython\u8f93\u51fa
\n\u5b57\u5178\u8bbe\u8ba1\u63a8\u7b97
\n\u5c1a\u672a\u6267\u884c\u7684OpenFOAM\u64cd\u4f5c <\/p>\n \u5341\u56db\u3001\u672c\u8282\u5c0f\u7ed3\u4e0e\u4e0b\u4e00\u8282<\/h3>\n\u53ef\u9760\u7684CFD\u8bbe\u7f6e，\u4e0d\u662f\u7b80\u5355\u5730\u628a\u7f51\u683c\u52a0\u5bc6\u3001\u65f6\u95f4\u6b65\u7f29\u5c0f\u3001\u6b8b\u5dee\u538b\u4f4e，\u800c\u662f\u8ba9\u6bcf\u4e2a\u8bbe\u7f6e\u670d\u52a1\u4e8e\u540c\u4e00\u4e2a\u6b63\u786e\u7269\u7406\u95ee\u9898\u3002<\/p>\n \u672c\u8282\u6700\u91cd\u8981\u7684\u8ba4\u8bc6\u662f：<\/p>\n \u7f51\u683c\u8d28\u91cf\u3001\u8fb9\u754c\u6b63\u786e\u6027\u3001\u7a7a\u95f4\u8bef\u5dee\u3001\u65f6\u95f4\u8bef\u5dee\u548c\u8fed\u4ee3\u8bef\u5dee，\u9700\u8981\u5206\u522b\u68c0\u67e5，\u4e0d\u80fd\u5f7c\u6b64\u66ff\u4ee3\u3002<\/p>\n \u4e0b\u4e00\u8282\u5c06\u6309\u7167\u8bfe\u7a0b\u76ee\u5f55，\u8fdb\u5165\u201cOpenFOAM\u5de5\u4f5c\u6d41\u81ea\u52a8\u5316\u201d，\u628a\u7f51\u683c\u751f\u6210\u3001\u7f51\u683c\u68c0\u67e5\u3001\u6c42\u89e3\u3001\u540e\u5904\u7406\u548c\u505c\u6b62\u6761\u4ef6\u7ec4\u7ec7\u8d77\u6765\u3002<\/p>\n","protected":false},"excerpt":{"rendered":" \u8bfe\u7a0b\u6458\u8981
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