{"id":1008,"date":"2025-11-18T15:07:54","date_gmt":"2025-11-18T07:07:54","guid":{"rendered":"https:\/\/guagefangzhen.cn\/?p=1008"},"modified":"2025-12-05T14:39:03","modified_gmt":"2025-12-05T06:39:03","slug":"%e7%9b%b8%e5%9c%ba%e6%b3%95%e5%9c%a8-comsol-%e4%b8%ad%e7%9a%84%e5%ba%94%e7%94%a8%ef%bc%9a%e4%bb%8e%e5%9f%ba%e7%a1%80%e5%88%b0%e5%89%8d%e6%b2%bf","status":"publish","type":"post","link":"https:\/\/guagefangzhen.cn\/?p=1008","title":{"rendered":"\u76f8\u573a\u6cd5\u5728 COMSOL \u4e2d\u7684\u5e94\u7528\uff1a\u4ece\u57fa\u7840\u5230\u524d\u6cbf"},"content":{"rendered":"\n<p><em>\u5173\u952e\u8bcd\uff1a\u76f8\u573a\u6cd5\u3001COMSOL\u3001\u591a\u76f8\u6d41\u3001\u754c\u9762\u8ffd\u8e2a\u3001Cahn-Hilliard\u3001\u9502\u679d\u6676\u3001T \u578b\u5fae\u901a\u9053\u3001\u62d3\u6251\u53d8\u5316<\/em><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1 \u4ec0\u4e48\u662f\u76f8\u573a\u6cd5\uff1f\u5b83\u80fd\u505a\u4ec0\u4e48\uff1f<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">1.1 \u5b9a\u4e49<\/h4>\n\n\n\n<p>\u76f8\u573a\u6cd5\uff08Phase-Field Method, PFM\uff09\u7528\u4e00\u6761\u201c\u5f25\u6563\u754c\u9762\u201d\u4ee3\u66ff\u4f20\u7edf\u5c16\u9510\u754c\u9762\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5f15\u5165\u5e8f\u53c2\u91cf \u03d5\uff080\u21921\uff09\uff0c\u5728\u754c\u9762\u9644\u8fd1\u8fde\u7eed\u7a81\u53d8\uff1b<\/li>\n\n\n\n<li>\u754c\u9762\u4f4d\u7f6e = \u7b49\u503c\u9762\uff08\u5982 \u03d5=0.5\uff09\uff0c\u65e0\u9700\u663e\u5f0f\u8ffd\u8e2a\uff1b<\/li>\n\n\n\n<li>\u6f14\u5316\u7531\u4e00\u5bf9\u6216\u4e00\u7ec4 PDE \u63a7\u5236\uff08Cahn-Hilliard\u3001Allen-Cahn\u3001\u8026\u5408 Navier-Stokes\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">1.2 \u5178\u578b\u5e94\u7528<\/h4>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u9886\u57df<\/th><th>\u573a\u666f\u4e3e\u4f8b<\/th><th>\u76f8\u573a\u80fd\u6355\u6349\u7684\u5173\u952e\u73b0\u8c61<\/th><\/tr><\/thead><tbody><tr><td>\u6750\u6599<\/td><td>\u51dd\u56fa\u3001\u518d\u7ed3\u6676\u3001\u6790\u51fa\u3001\u9502\u679d\u6676<\/td><td>\u6676\u754c\u8fc1\u79fb\u3001\u679d\u6676\u5206\u53c9\u3001\u6676\u7c92\u7c97\u5316<\/td><\/tr><tr><td>\u6d41\u4f53<\/td><td>\u5fae\u6d41\u63a7\u6db2\u6ef4\u3001\u6c14\u6ce1\u7834\u788e\u3001\u6cb9\u6c34\u9a71\u66ff<\/td><td>\u62d3\u6251\u53d8\u5316\u3001\u8868\u9762\u5f20\u529b\u4e3b\u5bfc\u6d41\u52a8<\/td><\/tr><tr><td>\u751f\u7269<\/td><td>\u80bf\u7624\u751f\u957f\u3001\u7ec6\u80de\u805a\u96c6<\/td><td>\u754c\u9762\u5931\u7a33\u3001\u5f62\u6001\u53d1\u751f<\/td><\/tr><tr><td>\u5316\u5b66<\/td><td>\u53cd\u5e94-\u6269\u6563-\u76f8\u5206\u79bb\u8026\u5408<\/td><td>\u56fe\u6848\u5f62\u6210\u3001\u6eb6\u80f6-\u51dd\u80f6\u8f6c\u53d8<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u4e00\u53e5\u8bdd\uff1a\u53ea\u8981\u95ee\u9898\u91cc\u51fa\u73b0\u201c\u754c\u9762\u5728\u52a8\u3001\u5f62\u8c8c\u5728\u53d8\u3001\u8868\u9762\u5f20\u529b\u8bf4\u4e86\u7b97\u201d\uff0c\u76f8\u573a\u6cd5\u5c31\u80fd\u6d3e\u4e0a\u7528\u573a\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2 COMSOL \u4e2d\u7684\u76f8\u573a\u4eff\u771f\uff1a\u5f00\u7bb1\u5373\u7528\u7684\u6a21\u5757<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">2.1 \u5b98\u65b9\u63a5\u53e3<\/h4>\n\n\n\n<p>Multiphysics 5.6 \u4e4b\u540e\u5185\u7f6e \u201cPhase Field\u201d \u5206\u652f\uff0c\u63d0\u4f9b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Cahn-Hilliard Equation<\/strong> \u63a5\u53e3\uff08\u56db\u9636\uff0c\u4fdd\u5b88\u573a\uff09\uff1b<\/li>\n\n\n\n<li><strong>Two-Phase Flow, Phase Field<\/strong> \u63a5\u53e3\uff08\u8026\u5408 Navier-Stokes\uff0c\u81ea\u52a8\u7ed9\u51fa\u8868\u9762\u5f20\u529b\u6e90\u9879\uff09\uff1b<\/li>\n\n\n\n<li>\u4e0e<strong>\u6e4d\u6d41\u3001\u4f20\u70ed\u3001\u7535\u5316\u5b66\u3001\u6d53\u7269\u8d28\u4f20\u9012<\/strong>\u7b49\u4efb\u610f\u8026\u5408\u3002<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">2.2 \u4ee3\u8868\u6848\u4f8b\uff08\u5df2\u9a8c\u8bc1\u53ef\u76f4\u63a5\u590d\u73b0\uff09<\/h4>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u6848\u4f8b<\/th><th>\u5173\u952e\u8bbe\u7f6e<\/th><th>\u7ed3\u679c\u4eae\u70b9<\/th><\/tr><\/thead><tbody><tr><td>T \u578b\u5fae\u901a\u9053\u4e73\u6db2\u751f\u6210<\/td><td>\u4e8c\u7ef4\/\u4e09\u7ef4\u5c42\u6d41 + \u76f8\u573a\uff0c\u6bdb\u7ec6\u6570 Ca=0.01<\/td><td>\u65e0\u9700\u52a8\u7f51\u683c\u5373\u53ef\u6355\u6349\u6ef4\u72b6-\u5c04\u6d41\u8f6c\u6362<\/td><\/tr><tr><td>\u591a\u5b54\u4ecb\u8d28\u6c34-\u6c14\u9a71\u66ff<\/td><td>Brinkman + \u76f8\u573a\uff0c\u63a5\u89e6\u89d2 \u03b8=45\u00b0<\/td><td>\u53ef\u89c6\u5316\u6307\u8fdb\u3001\u6b8b\u4f59\u6c14\u9971\u548c\u5ea6<\/td><\/tr><tr><td>\u9502\u679d\u6676\u751f\u957f<\/td><td>\u7535\u5316\u5b66 + \u76f8\u573a\uff0c\u8fc7\u7535\u4f4d 50 mV<\/td><td>\u8f93\u51fa 3D \u679d\u6676\u52a8\u753b\uff0c\u4e0e\u5b9e\u9a8c\u5f62\u8c8c\u543b\u5408<\/td><\/tr><tr><td>\u975e\u725b\u987f\u6d41\u4f53\u6c14\u6ce1\u4e0a\u5347<\/td><td>\u5361\u68ee\u6a21\u578b + \u76f8\u573a<\/td><td>\u9ad8\u9ecf\u6db2\u4f53\u4e2d\u201c\u5c3e\u5df4\u201d\u65ad\u88c2\u9996\u6b21\u6570\u503c\u518d\u73b0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u5728 COMSOL \u4e2d\uff0c\u7528\u6237\u53ea\u9700\uff1a\u2460\u9009\u63a5\u53e3\uff1b\u2461\u586b\u7269\u6027\uff08\u03c3\u3001\u03b5\u3001M\uff09\uff1b\u2462\u753b\u7f51\u683c\uff1b\u2463\u8dd1\u77ac\u6001\u2014\u2014\u5373\u53ef\u5728\u51e0\u5c0f\u65f6\u5185\u5f97\u5230\u53ef\u53d1\u8868\u7ea7\u522b\u7684\u754c\u9762\u6f14\u5316\u52a8\u753b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3 COMSOL vs. \u5176\u4ed6\u5b9e\u73b0\u8def\u7ebf\uff1a\u4f18\u52a3\u52bf\u901f\u89c8<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u7ef4\u5ea6<\/th><th>COMSOL \u76f8\u573a<\/th><th>\u81ea\u7f16\u7a0b\uff08FEniCS\/MOOSE\uff09<\/th><th>\u5f00\u6e90\u5305\uff08OpenFOAM-isoAdvector\uff09<\/th><th>\u6c34\u5e73\u96c6\/VOF\uff08Fluent\uff09<\/th><\/tr><\/thead><tbody><tr><td>\u5f00\u53d1\u901f\u5ea6<\/td><td>\u2605\u2605\u2605\u2605\u2605 \u62d6\u62fd\u5f0f<\/td><td>\u2605 \u9700\u5199\u5f31\u5f62\u5f0f+\u5e76\u884c<\/td><td>\u2605\u2605 \u9700\u6539\u5e93+C++<\/td><td>\u2605\u2605\u2605 UDF \u811a\u672c<\/td><\/tr><tr><td>\u62d3\u6251\u53d8\u5316<\/td><td>\u81ea\u52a8\u5904\u7406<\/td><td>\u81ea\u52a8\u5904\u7406<\/td><td>\u9700 reconnect<\/td><td>\u9700\u8026\u5408\u7b97\u6cd5<\/td><\/tr><tr><td>\u8868\u9762\u5f20\u529b\u7cbe\u5ea6<\/td><td>\u4e8c\u9636\u4e00\u81f4\uff0c\u53ef\u8c03 \u03b5<\/td><td>\u9ad8\u9636\u5143\u53ef\u8fbe\u56db\u9636<\/td><td>\u8868\u9762\u5f20\u529b\u7b97\u5b50\u96be\u8c03<\/td><td>\u8fde\u7eed\u8868\u9762\u529b\uff0c\u8017\u6563\u5927<\/td><\/tr><tr><td>\u591a\u7269\u7406\u8026\u5408<\/td><td>\u4e00\u952e\u8026\u5408\u4efb\u610f\u573a<\/td><td>\u9700\u624b\u5de5\u52a0\u65b9\u7a0b<\/td><td>\u9700\u6539 solver<\/td><td>\u9700 UDF \u6216 Scheme<\/td><\/tr><tr><td>\u7f51\u683c\u81ea\u9002\u5e94<\/td><td>\u5185\u7f6e h-adapt<\/td><td>\u53ef\u642d ALBERTA<\/td><td>\u65e0\u5b98\u65b9 r-adapt<\/td><td>VOF \u53ea\u80fd\u5c40\u90e8\u7ec6\u5316<\/td><\/tr><tr><td>licence<\/td><td>\u5546\u4e1a<\/td><td>\u514d\u8d39<\/td><td>\u514d\u8d39<\/td><td>\u5546\u4e1a<\/td><\/tr><tr><td>\u5e76\u884c\u89c4\u6a21<\/td><td>\u684c\u9762-256 \u6838<\/td><td>\u8d85\u7b97\u4e07\u6838<\/td><td>\u5343\u6838<\/td><td>\u5343\u6838<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u4e00\u53e5\u8bdd\u603b\u7ed3\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u201c\u60f3\u5feb\u901f\u53d1\u8bba\u6587\/\u505a\u53ef\u884c\u6027\u9a8c\u8bc1\u201d<\/strong> \u2192 \u9009 COMSOL\uff1b<\/li>\n\n\n\n<li><strong>\u201c\u60f3\u73a9\u7b97\u6cd5\u3001\u8c03\u683c\u5f0f\u3001\u8dd1\u767e\u4e07\u6838\u201d<\/strong> \u2192 \u81ea\u7f16\u7a0b\u6216 MOOSE\uff1b<\/li>\n\n\n\n<li><strong>\u201c\u53ea\u505a\u5b8f\u89c2\u5927\u5c3a\u5ea6\u3001\u6e4d\u6d41\u4e3a\u4e3b\u201d<\/strong> \u2192 Fluent+VOF\/\u6c34\u5e73\u96c6 \u8db3\u591f\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">4 \u8fd1\u671f\u53d1\u5c55\u4e0e\u672a\u6765\u5c55\u671b\uff082025-2030\uff09<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">4.1 \u7b97\u6cd5\u70ed\u70b9<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6df1\u5ea6\u5b66\u4e60\u52a0\u901f\u76f8\u573a<\/strong> \u2013 Physics-Informed CNN \u66ff\u4ee3\u9ad8\u9636\u7f51\u683c\uff0c\u8bad\u7ec3\u4e00\u6b21\u63a8\u7406\u5343\u6b21\uff0c\u8ba1\u7b97\u91cf \u219390%\u3002<\/li>\n\n\n\n<li><strong>\u81ea\u9002\u5e94\u7f51\u683c + \u591a\u91cd\u7f51\u683c\u6c42\u89e3\u5668<\/strong> \u2013 COMSOL 2025 \u65b0 beta \u529f\u80fd\uff1a\u4f34\u968f\u654f\u5ea6\u9a71\u52a8\u81ea\u9002\u5e94\uff0c\u03b5 \u5c40\u90e8\u7ec6\u5316\u5230 0.1 \u03bcm\uff0c\u5185\u5b58 \u219360%\u3002<\/li>\n\n\n\n<li><strong>\u9ad8\u9636\u71b5\u7a33\u5b9a\u683c\u5f0f<\/strong> \u2013 \u4fdd\u8bc1\u80fd\u91cf\u9012\u51cf\uff0c\u65f6\u95f4\u6b65\u957f\u63d0\u5347 5\u00d7\uff0c\u5df2\u7528\u4e8e\u9502\u679d\u6676 3D \u6a21\u62df\u3002<\/li>\n\n\n\n<li><strong>\u5f02\u6784\u8ba1\u7b97<\/strong> \u2013 GPU \u7a00\u758f\u77e9\u9635\u6c42\u89e3\u5668\uff08NVIDIA AmgX\uff09\u96c6\u6210\uff0c\u5355\u5361 A100 \u901f\u5ea6 \u2248 200 CPU \u6838\u3002<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">4.2 \u5e94\u7528\u5c55\u671b<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u56fa\u6001\u7535\u6c60<\/strong>\uff1a\u76f8\u573a-\u529b\u5b66-\u7535\u5316\u5b66\u8026\u5408\uff0c\u9884\u6d4b\u754c\u9762\u7a7a\u6d1e\u2192\u679d\u6676\u2192\u77ed\u8def\u5168\u94fe\uff1b<\/li>\n\n\n\n<li><strong>\u91d1\u5c5e 3D \u6253\u5370<\/strong>\uff1a\u7194\u6c60-\u6676\u7c92-\u76f8\u573a\u8054\u5408\uff0c\u5b9e\u65f6\u9884\u6d4b\u5b54\u9699\u7f3a\u9677\uff1b<\/li>\n\n\n\n<li><strong>\u78b3\u5c01\u5b58<\/strong>\uff1aCO\u2082-\u6c34-\u5ca9\u77f3\u4e09\u76f8\u76f8\u573a\uff0c\u8bc4\u4f30\u76d6\u5c42\u6307\u8fdb\u98ce\u9669\uff1b<\/li>\n\n\n\n<li><strong>\u751f\u7269\u533b\u5b66<\/strong>\uff1a\u80bf\u7624-\u8840\u7ba1-\u836f\u7269\u4e09\u76f8\u6a21\u578b\uff0c\u6307\u5bfc\u7eb3\u7c73\u9897\u7c92\u9012\u9001\uff1b<\/li>\n\n\n\n<li><strong>\u5fae\u6d41\u63a7 AI \u8bbe\u8ba1<\/strong>\uff1a\u76f8\u573a\u4eff\u771f\u4f5c\u6570\u5b57\u5b6a\u751f\uff0c\u5728\u7ebf\u95ed\u73af\u4f18\u5316\u6db2\u6ef4\u5c3a\u5bf8\u3002<\/li>\n<\/ul>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u9884\u8ba1 2030 \u5e74\u524d\uff0c\u76f8\u573a\u6cd5\u5c06\u4ece\u201c\u9ad8\u7aef\u79d1\u7814\u201d\u4e0b\u6c89\u4e3a\u201c\u5de5\u4e1a\u6807\u914d\u201d\uff0cCOMSOL \u7b49\u5546\u4e1a\u5e73\u53f0\u5c06\u63d0\u4f9b\u4e00\u952e\u5f0f\u201c\u76f8\u573a App\u201d\uff0c\u8ba9\u5de5\u827a\u5de5\u7a0b\u5e08\u50cf\u4eca\u5929\u5f00 Excel \u4e00\u6837\u505a\u754c\u9762\u6f14\u5316\u5206\u6790\u3002<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\">5 \u5feb\u901f\u4e0a\u624b\u6307\u5357\uff08\u5f69\u86cb\uff09<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u6253\u5f00 COMSOL \u2192 \u6a21\u578b\u5411\u5bfc \u2192 \u9009\u62e9\u201c\u4e8c\u76f8\u6d41\uff0c\u76f8\u573a\u201d\u63a5\u53e3\uff1b<\/li>\n\n\n\n<li>\u6750\u6599\u5e93\u76f4\u63a5\u641c\u201cWater\u201d&amp;\u201cAir\u201d\uff0c\u8868\u9762\u5f20\u529b 0.073 N\/m \u81ea\u52a8\u8f7d\u5165\uff1b<\/li>\n\n\n\n<li>\u51e0\u4f55\u753b\u4e00\u4e2a\u201cT \u578b\u201d\u5fae\u901a\u9053\uff08\u5bbd 100 \u03bcm\uff09\uff0c\u5165\u53e3\u901f\u5ea6 0.1 m\/s\uff1b<\/li>\n\n\n\n<li>\u7f51\u683c \u2192 \u7269\u7406\u573a\u63a7\u5236 \u2192 \u6781\u7ec6\u5316\uff0c\u754c\u9762\u533a\u81ea\u52a8\u52a0\u5bc6\uff1b<\/li>\n\n\n\n<li>\u77ac\u6001\u6c42\u89e3 0\u20130.02 s\uff0c\u6b65\u957f 1e-4 s\uff0c\u70b9\u51fb\u8ba1\u7b97\u219210 min \u540e\u6536\u83b7\u9ad8\u6e05\u4e73\u6db2\u751f\u6210\u52a8\u753b\uff01<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u7ed3\u8bed<\/h3>\n\n\n\n<p>\u76f8\u573a\u6cd5\u628a\u201c\u754c\u9762\u201d\u53d8\u6210\u201c\u573a\u201d\uff0c\u8ba9\u62d3\u6251\u53d8\u5316\u4e0d\u518d\u662f\u5669\u68a6\uff1b<br>COMSOL 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