{"id":1097,"date":"2026-01-29T17:16:34","date_gmt":"2026-01-29T09:16:34","guid":{"rendered":"https:\/\/guagefangzhen.cn\/?p=1097"},"modified":"2026-02-09T15:13:41","modified_gmt":"2026-02-09T07:13:41","slug":"comsol-cfd-%e5%a3%81%e9%9d%a2%e6%bb%91%e7%a7%bb%e5%85%a8%e5%ae%b6%e6%a1%b6%e8%af%a6%e8%a7%a3-%e4%bb%8e-no-slip-%e5%88%b0-rarefied-gas%ef%bc%8c%e4%b8%80%e7%af%87","status":"publish","type":"post","link":"https:\/\/guagefangzhen.cn\/?p=1097","title":{"rendered":"COMSOL CFD \u58c1\u9762\u6ed1\u79fb\u201c\u5168\u5bb6\u6876\u201d\u8be6\u89e3\u2014\u2014\u4ece No-Slip \u5230 Rarefied Gas\uff0c\u4e00\u7bc7\u5c31\u591f"},"content":{"rendered":"\n

\u5728\u7edd\u5927\u591a\u6570\u5b8f\u89c2\u6d41\u52a8\u6a21\u62df\u91cc\uff0c\u6211\u4eec\u90fd\u9ed8\u8ba4\u201c\u58c1\u9762\u65e0\u6ed1\u79fb\u201d\u2014\u2014\u6d41\u4f53\u5fae\u56e2\u4e00\u65e6\u8d34\u4e0a\u58c1\u9762\uff0c\u5c31\u53ea\u80fd\u4e56\u4e56\u8ddf\u7740\u58c1\u9762\u8d70\uff0c\u901f\u5ea6\u5dee\u4e3a\u96f6\u3002\u7136\u800c\u5f53\u6d41\u52a8\u5c3a\u5ea6\u7f29\u5c0f\u5230\u5fae\u7c73\u3001\u7eb3\u7c73\uff0c\u6216\u8005\u6c14\u4f53\u7a00\u8584\u5230\u5e73\u5747\u81ea\u7531\u7a0b\u4e0e\u7279\u5f81\u5c3a\u5ea6\u53ef\u6bd4\u62df\u65f6\uff0c\u58c1\u9762\u5206\u5b50\u4e0e\u6d41\u4f53\u5206\u5b50\u4e4b\u95f4\u7684\u52a8\u91cf\u4ea4\u6362\u4e0d\u518d\u201c\u5b8c\u7f8e\u201d\uff0c\u4e8e\u662f\u6d41\u4f53\u5728\u58c1\u9762\u5904\u4f1a\u51fa\u73b0\u4e00\u5c42\u53ef\u5bdf\u89c9\u7684\u5207\u5411\u901f\u5ea6\u5dee\uff0c\u8fd9\u79cd\u73b0\u8c61\u5c31\u53eb\u58c1\u9762\u6ed1\u79fb\uff08wall slip\uff09\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u5b83\u672c\u8d28\u4e0a\u662f\u4e00\u6761\u201c\u8fb9\u754c\u5904\u7684\u901f\u5ea6\u4e0d\u8fde\u7eed\u201d\uff0c\u5176\u5927\u5c0f\u901a\u5e38\u7528\u6ed1\u79fb\u957f\u5ea6 b \u6765\u91cf\u5316\uff1a
u_slip = b \u00b7 (\u2202u\/\u2202n)|wall
\u5176\u4e2d b \u5177\u6709\u957f\u5ea6\u91cf\u7eb2\uff0c\u53ef\u89c6\u4e3a\u201c\u628a\u901f\u5ea6\u5256\u9762\u7ebf\u6027\u5916\u63a8\u5230\u96f6\u201d\u65f6\u4e0e\u58c1\u9762\u7684\u8ddd\u79bb\u3002\u6ed1\u79fb\u957f\u5ea6\u8d8a\u5927\uff0c\u58c1\u9762\u7ed9\u6d41\u4f53\u7684\u201c\u6469\u64e6\u529b\u201d\u5c31\u8d8a\u5c0f\uff0c\u5b8f\u89c2\u4e0a\u8868\u73b0\u4e3a\u51cf\u963b\u3001\u6d41\u91cf\u589e\u5927\u6216\u538b\u964d\u964d\u4f4e\u3002<\/p>\n\n\n\n

CFD \u8ba1\u7b97\u4e2d\u5982\u4f55\u628a\u201c\u6ed1\u79fb\u201d\u5199\u8fdb\u4ee3\u7801\uff1f<\/p>\n\n\n\n

    \n
  1. \u8fb9\u754c\u6761\u4ef6\u66ff\u6362 \u5728\u52a8\u91cf\u65b9\u7a0b\u79bb\u6563\u540e\u7684\u7ebf\u6027\u7cfb\u7edf\u91cc\uff0c\u65e0\u6ed1\u79fb\u76f8\u5f53\u4e8e\u628a\u58c1\u9762\u8282\u70b9\u901f\u5ea6\u76f4\u63a5\u9489\u6b7b\uff08Dirichlet\uff09\u3002\u6ed1\u79fb\u5219\u628a\u8be5\u8282\u70b9\u901f\u5ea6\u4f5c\u4e3a\u672a\u77e5\u91cf\uff0c\u628a\u6ed1\u79fb\u957f\u5ea6\u6216\u526a\u5207\u5e94\u529b\u5199\u8fdb\u77e9\u9635\u7684\u4e00\u884c\uff0c\u53d8\u6210 Robin \u578b\u6761\u4ef6\uff1a \u03bc\u00b7(\u2202u\/\u2202n) = C\u00b7(u_wall \u2212 u_fluid) \u5176\u4e2d C = \u03bc\/b\uff0cb \u4e3a\u6ed1\u79fb\u957f\u5ea6\u3002<\/li>\n\n\n\n
  2. \u8fd1\u58c1\u7f51\u683c\u5904\u7406 \u82e5\u91c7\u7528\u4f4e Re \u6e4d\u6d41\u6a21\u578b\u6216\u5c42\u6d41\u89e3\u6790\uff0c\u58c1\u9762\u7b2c\u4e00\u5c42\u7f51\u683c\u9ad8\u5ea6 \u0394y \u5e94\u4fdd\u8bc1 y\u207a\u22481\uff0c\u5426\u5219\u6ed1\u79fb\u91cf\u4f1a\u88ab\u6570\u503c\u9ecf\u6027\u201c\u5403\u6389\u201d\uff1b\u82e5\u7528\u5927\u6da1\/\u96f7\u8bfa\u5e73\u5747\uff0c\u5219\u9700\u5728\u58c1\u9762\u51fd\u6570\u91cc\u628a \u0394u\u207a \u7684\u4fee\u6b63\u9879\u663e\u5f0f\u5199\u51fa\uff0c\u4f8b\u5982\u5bf9\u6570\u5f8b\u53e0\u52a0 \u0394u\u207a(b\u207a)\u3002<\/li>\n\n\n\n
  3. \u591a\u5c3a\u5ea6\u8026\u5408 \u5bf9\u5fae\u6c9f\u69fd\u3001\u591a\u5b54\u6d82\u5c42\u7b49\u573a\u666f\uff0c\u53ef\u5148\u7528\u683c\u5b50-\u73bb\u5c14\u5179\u66fc\u6216 MD \u7b97\u51fa b \u4e0e\u5b8f\u89c2\u53c2\u6570\uff08\u526a\u5207\u7387\u3001\u538b\u529b\u3001\u6e29\u5ea6\uff09\u7684\u6570\u636e\u5e93\uff0c\u518d\u7528\u795e\u7ecf\u7f51\u7edc\u62df\u5408\u6210\u201c\u6ed1\u79fb\u8fb9\u754c\u51fd\u6570\u201d\uff0c\u5728\u5b8f\u89c2 RANS\/LES \u6c42\u89e3\u5668\u91cc\u4ee5\u81ea\u5b9a\u4e49\u8fb9\u754c\u6761\u4ef6\u7684\u65b9\u5f0f\u8c03\u7528\u3002<\/li>\n<\/ol>\n\n\n\n

    COMSOL \u91cc\u80fd\u7528\u7684\u201c\u6ed1\u79fb\u201d\u5957\u9910
    COMSOL \u628a\u6ed1\u79fb\u73b0\u8c61\u62c6\u6210\u4e09\u6761\u4e3b\u7ebf\uff0c\u5206\u522b\u5728\u201c\u5c42\u6d41\u201d\u3001\u201c\u6ed1\u79fb\u6d41\u201d\u548c\u201c\u7a00\u5e03\/\u5206\u5b50\u6d41\u201d\u63a5\u53e3\u4e2d\u5f00\u7bb1\u5373\u7528\uff1a<\/p>\n\n\n\n

      \n
    1. \u901a\u7528\u201c\u6ed1\u79fb\u201d\u8fb9\u754c \u4f4d\u7f6e\uff1a\u5c42\u6d41 \u2192 \u58c1 \u2192 \u6ed1\u79fb \u6570\u5b66\u5f62\u5f0f\uff1a \u03c4_t = \u2212 (\u03bc\/b)\u00b7(u_t \u2212 u_wall) \u7528\u6237\u53ea\u9700\u586b\u4e00\u4e2a\u201c\u6ed1\u79fb\u957f\u5ea6\u201d b\uff0c\u53ef\u8bbe\u4e3a\u5e38\u6570\u3001\u8868\u8fbe\u5f0f\u6216\u968f\u573a\u53d8\u91cf\u51fd\u6570\u3002\u82e5 b\u21920\uff0c\u81ea\u52a8\u9000\u5316\u4e3a\u65e0\u6ed1\u79fb\uff1b\u82e5 b\u2192\u221e\uff0c\u5219\u9000\u5316\u4e3a\u5b8c\u5168\u6ed1\u79fb\uff08\u526a\u5207\u5e94\u529b\u4e3a\u96f6\uff09\u3002 \u9002\u7528\uff1a\u5fae\u901a\u9053\u6db2\u4f53\u3001\u805a\u5408\u7269\u6324\u51fa\u3001\u4f4e\u6e17\u900f\u591a\u5b54\u58c1\u7b49\u3002<\/li>\n\n\n\n
    2. \u589e\u5f3a Navier \u6ed1\u79fb\uff08\u7528\u6237\u81ea\u5b9a\u4e49\uff09 \u5f53\u6ed1\u79fb\u957f\u5ea6\u4e0e\u526a\u5207\u7387\u672c\u8eab\u76f8\u5173\u65f6\uff08\u5982\u7c98\u5f39\u6027\u7194\u4f53\uff09\uff0c\u53ef\u5728\u201c\u5f31\u8d21\u732e\u201d\u91cc\u5199\u5165\uff1a b = b\u2080\u00b7|\u03b3\u0307|^(n-1) \u628a \u03c4_t = \u2212 (\u03bc\/b)\u00b7u_t \u4f5c\u4e3a\u9644\u52a0\u5f31\u5f62\u5f0f\u79ef\u5206\u5230\u58c1\u9762\u5355\u5143\u4e0a\uff0c\u5b9e\u73b0\u526a\u5207\u4f9d\u8d56\u6ed1\u79fb\u3002<\/li>\n\n\n\n
    3. \u6ed1\u79fb\u6d41\u63a5\u53e3\uff08Kn 0.001\u20130.1\uff09 \u4f4d\u7f6e\uff1a\u7a00\u6709fied flow \u2192 Slip flow \u58c1\u9762\u81ea\u52a8\u52a0\u8f7d Maxwell \u70ed-\u8d28\u6ed1\u79fb\u516c\u5f0f\uff1a u_s = \u03c3_p\u00b7\u03bb\/\u03bc\u00b7\u03c4_t + \u03c3_T\u00b7\u03bc\/(\u03c1T)\u00b7\u2207T_t T_gas \u2212 T_wall = \u03b6_T\u00b7\u03bb\u00b7(\u2202T\/\u2202n) \u5176\u4e2d \u03bb \u4e3a\u5e73\u5747\u81ea\u7531\u7a0b\uff0c\u03c3_p\u3001\u03c3_T\u3001\u03b6_T \u7531\u201c\u5207\u5411\u52a8\u91cf\u8c03\u8282\u7cfb\u6570\u201d\u03b1 \u8ba1\u7b97\u800c\u6765\uff0c\u6750\u6599\u5e93\u5df2\u5185\u7f6e\u7a7a\u6c14\u3001\u6c2e\u6c14\u7b49\u53c2\u6570\u3002 \u8be5\u63a5\u53e3\u540c\u65f6\u628a\u8fde\u7eed\u6027\u3001\u52a8\u91cf\u3001\u80fd\u91cf\u65b9\u7a0b\u5728\u514b\u52aa\u68ee\u5c42\u5916\u6c42\u89e3\uff0c\u7701\u53bb\u89e3\u6790\u7eb3\u7c73\u7ea7\u8fb9\u754c\u5c42\u7684\u7f51\u683c\u8d1f\u62c5\u3002<\/li>\n\n\n\n
    4. \u5206\u5b50\u6d41\/\u8fc7\u6e21\u6d41\uff08Kn>0.1\uff09 \u82e5\u901a\u9053\u5c3a\u5bf8\u7ee7\u7eed\u7f29\u5c0f\uff0cCOMSOL \u63d0\u4f9b\u201c\u5206\u5b50\u6d41\u201d\u6a21\u5757\uff0c\u91c7\u7528\u7ebf-of-sight \u6216 DSMC \u65b9\u6cd5\uff0c\u628a\u58c1\u9762\u89c6\u4e3a\u6f2b\u53cd\u5c04\/\u955c\u9762\u53cd\u5c04\u8868\u9762\uff0c\u6ed1\u79fb\u6548\u5e94\u5df2\u9690\u542b\u5728\u6563\u5c04\u6838\u91cc\uff0c\u65e0\u9700\u518d\u989d\u5916\u6307\u5b9a\u6ed1\u79fb\u957f\u5ea6\u3002<\/li>\n<\/ol>\n\n\n\n

      \u5c0f\u7ed3
      \u58c1\u9762\u6ed1\u79fb\u4e0d\u662f\u201c\u7384\u5b66\u201d\uff0c\u800c\u662f\u628a\u5206\u5b50\u5c3a\u5ea6\u52a8\u91cf\u4ea4\u6362\u7684\u5fae\u89c2\u4fe1\u606f\u538b\u7f29\u8fdb\u4e00\u4e2a\u201c\u53ef\u6d4b\u957f\u5ea6 b\u201d\u7684\u8fb9\u754c\u53c2\u6570\u3002\u53ea\u8981\u4f60\u7ed9\u51fa\u5408\u7406\u7684 b\uff08\u5b9e\u9a8c\u3001\u7406\u8bba\u6216\u8de8\u5c3a\u5ea6\u8ba1\u7b97\uff09\uff0c\u5728 COMSOL \u4e2d\u53ea\u9700\u4e00\u884c\u6ed1\u79fb\u957f\u5ea6\uff0c\u5c31\u80fd\u628a\u5fae\u7eb3\u5c3a\u5ea6\u7684\u51cf\u963b\u3001\u6d41\u91cf\u589e\u5f3a\u6216\u6e29\u5ea6\u8dc3\u53d8\u73b0\u8c61\u642c\u5230\u5b8f\u89c2\u6c42\u89e3\u5668\u91cc\uff1b\u5f53\u514b\u52aa\u68ee\u6570\u518d\u5f80\u4e0a\u8d70\uff0c\u5c31\u6362\u7528\u66f4\u5e95\u5c42\u7684\u6ed1\u79fb\u6d41\u6216\u5206\u5b50\u6d41\u63a5\u53e3\uff0c\u8ba9 Maxwell \u6216 DSMC \u5e2e\u4f60\u81ea\u52a8\u5904\u7406\u90a3\u5c42\u201c\u4e0d\u542c\u8bdd\u201d\u7684\u8fb9\u754c\u3002\u795d\u4f60\u5728\u4e0b\u4e00\u6b21\u4eff\u771f\u91cc\uff0c\u65e2\u80fd\u6293\u4f4f\u8fb9\u754c\u5c42\uff0c\u53c8\u4e0d\u88ab\u8fb9\u754c\u5c42\u201c\u54ac\u201d\u4f4f\u7f51\u683c\uff01<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      \u5728\u7edd\u5927\u591a\u6570\u5b8f\u89c2\u6d41\u52a8\u6a21\u62df\u91cc\uff0c\u6211\u4eec\u90fd\u9ed8\u8ba4\u201c\u58c1\u9762\u65e0\u6ed1\u79fb\u201d\u2014\u2014\u6d41\u4f53\u5fae\u56e2\u4e00\u65e6\u8d34\u4e0a\u58c1\u9762\uff0c\u5c31\u53ea\u80fd\u4e56\u4e56\u8ddf\u7740\u58c1\u9762\u8d70\uff0c\u901f\u5ea6\u5dee\u4e3a\u96f6\u3002 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[],"class_list":["post-1097","post","type-post","status-publish","format-standard","hentry","category-comsol"],"_links":{"self":[{"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=\/wp\/v2\/posts\/1097","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1097"}],"version-history":[{"count":1,"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=\/wp\/v2\/posts\/1097\/revisions"}],"predecessor-version":[{"id":1114,"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=\/wp\/v2\/posts\/1097\/revisions\/1114"}],"wp:attachment":[{"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1097"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1097"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1097"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}