{"id":1159,"date":"2026-03-27T16:57:09","date_gmt":"2026-03-27T08:57:09","guid":{"rendered":"https:\/\/guagefangzhen.cn\/?p=1159"},"modified":"2026-03-30T13:58:09","modified_gmt":"2026-03-30T05:58:09","slug":"%e4%bb%bf%e7%9c%9f%e5%b7%a5%e7%a8%8b%e5%b8%88%e5%bf%85%e6%87%82%ef%bc%9a%e5%81%8f%e5%af%bc%e3%80%81%e6%a2%af%e5%ba%a6%e3%80%81%e6%95%a3%e5%ba%a6%e3%80%81%e6%97%8b%e5%ba%a6%e3%80%81%e6%8b%89%e6%99%ae","status":"publish","type":"post","link":"https:\/\/guagefangzhen.cn\/?p=1159","title":{"rendered":"\u4eff\u771f\u5de5\u7a0b\u5e08\u5fc5\u61c2\uff1a\u504f\u5bfc\u3001\u68af\u5ea6\u3001\u6563\u5ea6\u3001\u65cb\u5ea6\u3001\u62c9\u666e\u62c9\u65af\uff5c\u751f\u6d3b\u4f8b\u5b50+\u6807\u51c6\u516c\u5f0f+COMSOL\u6848\u4f8b\u4e00\u7bc7\u6253\u901a"},"content":{"rendered":"\n

\uff08\u6709\u8da3\u4e0d\u6666\u6da9\u3001\u516c\u5f0f\u4e0d\u5413\u4eba\u3001\u770b\u5b8c\u80fd\u5206\u6e05\u3001\u5efa\u6a21\u7528\u5f97\u4e0a\uff09<\/p>\n\n\n\n

\u505a\u6709\u9650\u5143\u3001\u505a\u591a\u7269\u7406\u573a\u8026\u5408\uff0c\u504f\u5bfc\u3001\u68af\u5ea6\u3001\u6563\u5ea6\u3001\u65cb\u5ea6\u3001\u62c9\u666e\u62c9\u65af<\/strong>\u8fd9\u4e94\u4e2a\u8bcd\u5929\u5929\u89c1\u3002 \u6ee1\u5c4f\u7684 \u2202<\/mi><\/mrow>\\partial<\/annotation><\/semantics><\/math>\u2202\u3001\u2207<\/mi><\/mrow>\\nabla<\/annotation><\/semantics><\/math>\u2207\u3001\u2207<\/mi>\u22c5<\/mo><\/mrow>\\nabla\\cdot<\/annotation><\/semantics><\/math>\u2207\u22c5\u3001\u2207<\/mi>\u00d7<\/mo><\/mrow>\\nabla\\times<\/annotation><\/semantics><\/math>\u2207\u00d7\u3001\u0394<\/mi><\/mrow>\\Delta<\/annotation><\/semantics><\/math>\u0394\uff0c\u5230\u5e95\u5728\u8bf4\u5565\uff1f \u5b83\u4eec\u4e0d\u662f\u7384\u5b66\uff0c\u800c\u662f\u63cf\u8ff0\u4e16\u754c\u5982\u4f55\u53d8\u5316<\/strong>\u7684\u8bed\u8a00\uff1a \u70ed\u600e\u4e48\u4f20\u3001\u98ce\u600e\u4e48\u5439\u3001\u7535\u600e\u4e48\u8dd1\u3001\u6c34\u600e\u4e48\u65cb\u3001\u7ed3\u6784\u600e\u4e48\u5e73\u8861\uff0c\u5168\u9760\u5b83\u4eec\u3002 \u8fd9\u4e00\u7bc7\u628a\u8da3\u5473\u751f\u6d3b\u4f8b\u5b50 + \u6807\u51c6LaTeX\u516c\u5f0f + \u5de5\u7a0b\u610f\u4e49 + COMSOL\u771f\u5b9e\u6848\u4f8b<\/strong>\u63c9\u5728\u4e00\u8d77\uff0c \u8ba9\u4f60\u8bb0\u5f97\u4f4f\u3001\u5206\u5f97\u6e05\u3001\u7528\u5f97\u4e0a<\/strong>\u3002<\/p>\n\n\n\n
\n
\"\"<\/figure>\n<\/figure>\n\n\n\n

0\uff09\u603b\u7eb2\uff1a\u4e94\u53e5\u8bdd\u5148\u628a\u5b83\u4eec\u201c\u7ffb\u8bd1\u6210\u4eba\u8bdd\u201d<\/h2>\n\n\n\n
    \n
  • \u504f\u5bfc\u6570<\/strong>\uff1a\u53ea\u770b\u67d0\u4e00\u4e2a\u65b9\u5411\u7684\u53d8\u5316\u5feb\u6162<\/li>\n\n\n\n
  • \u68af\u5ea6<\/strong>\uff1a\u54ea\u6761\u8def\u6700\u9661\u3001\u53d8\u5316\u6700\u5feb\uff08\u573a\u7684\u9a71\u52a8\u529b\uff09<\/li>\n\n\n\n
  • \u6563\u5ea6<\/strong>\uff1a\u8fd9\u91cc\u662f\u55b7\u51fa\u6765\uff08\u6e90\uff09\u8fd8\u662f\u5438\u8fdb\u53bb\uff08\u6c47\uff09<\/li>\n\n\n\n
  • \u65cb\u5ea6<\/strong>\uff1a\u8fd9\u91cc\u6709\u6ca1\u6709\u6253\u8f6c\u3001\u6f29\u6da1\u3001\u65cb\u8f6c<\/li>\n\n\n\n
  • \u62c9\u666e\u62c9\u65af<\/strong>\uff1a\u573a\u662f\u51f8\u662f\u51f9\uff0c\u80fd\u4e0d\u80fd\u6162\u6162\u53d8\u5e73\u7a33\u3001\u8fbe\u5230\u5e73\u8861<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    1\uff09\u504f\u5bfc\u6570 Partial Derivative<\/h1>\n\n\n\n

    \u4e00\u53e5\u8bdd\u7406\u89e3<\/h3>\n\n\n\n

    \u53ea\u76ef\u4e00\u4e2a\u65b9\u5411\u770b\u53d8\u5316\uff0c\u5176\u4ed6\u65b9\u5411\u6682\u65f6\u201c\u51bb\u7ed3\u201d\u3002<\/strong><\/p>\n\n\n\n

    \u6807\u51c6\u516c\u5f0f\uff08\u4e09\u7ef4\u6807\u91cf\u573a u<\/mi>(<\/mo>x<\/mi>,<\/mo>y<\/mi>,<\/mo>z<\/mi>)<\/mo><\/mrow>u(x,y,z)<\/annotation><\/semantics><\/math>u(x,y,z)\uff09<\/h3>\n\n\n\n

    \u2202<\/mi>u<\/mi><\/mrow>\u2202<\/mi>x<\/mi><\/mrow><\/mfrac>,<\/mo><\/mspace>\u2202<\/mi>u<\/mi><\/mrow>\u2202<\/mi>y<\/mi><\/mrow><\/mfrac>,<\/mo><\/mspace>\u2202<\/mi>u<\/mi><\/mrow>\u2202<\/mi>z<\/mi><\/mrow><\/mfrac><\/mrow>\\frac{\\partial u}{\\partial x},\\quad \\frac{\\partial u}{\\partial y},\\quad \\frac{\\partial u}{\\partial z}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

    \u751f\u6d3b\/\u751f\u4ea7\u4f8b\u5b50<\/h3>\n\n\n\n
      \n
    • \u706b\u9505\uff1a\u53ea\u5173\u5fc3\u5de6\u53f3<\/strong>\u6e29\u5ea6\u5dee\u591a\u5c11<\/li>\n\n\n\n
    • \u7535\u6c60\u6563\u70ed\uff1a\u53ea\u770b\u539a\u5ea6\u65b9\u5411<\/strong>\u6e29\u5347\u5feb\u6162<\/li>\n\n\n\n
    • \u82af\u7247\uff1a\u53ea\u770b\u5782\u76f4\u57fa\u677f\u65b9\u5411<\/strong>\u70ed\u6d41\u53d8\u5316<\/li>\n<\/ul>\n\n\n\n

      \u4eff\u771f\u91cc\u7684\u4f5c\u7528<\/h3>\n\n\n\n

      \u6240\u6709\u659c\u7387\u3001\u65b9\u5411\u5bfc\u6570\u3001\u540e\u5904\u7406\u91cc\u7684\u201c\u67d0\u65b9\u5411\u5bfc\u6570\u201d\uff0c\u5e95\u5c42\u90fd\u662f\u504f\u5bfc\u3002<\/p>\n\n\n\n

      COMSOL\u8868\u8fbe\u5f0f<\/h3>\n\n\n\n

      d(T,x)<\/code>\u3001d(phi,y)<\/code><\/h2>\n\n\n\n

      2\uff09\u68af\u5ea6 Gradient \u2207u<\/h1>\n\n\n\n

      \u4e00\u53e5\u8bdd\u7406\u89e3<\/h3>\n\n\n\n

      \u6807\u91cf\u573a\u53d8\u5316\u6700\u9661\u7684\u65b9\u5411 + \u6700\u5927\u53d8\u5316\u7387\u3002<\/strong><\/p>\n\n\n\n

      \u68af\u5ea6 = \u573a\u7684\u201c\u9a71\u52a8\u529b\u201d\u3002<\/strong><\/p>\n\n\n\n

      \u6807\u51c6\u516c\u5f0f<\/h3>\n\n\n\n

      \u2207<\/mi>u<\/mi>=<\/mo>(<\/mo>\u2202<\/mi>u<\/mi><\/mrow>\u2202<\/mi>x<\/mi><\/mrow><\/mfrac>,<\/mo> <\/mtext>\u2202<\/mi>u<\/mi><\/mrow>\u2202<\/mi>y<\/mi><\/mrow><\/mfrac>,<\/mo> <\/mtext>\u2202<\/mi>u<\/mi><\/mrow>\u2202<\/mi>z<\/mi><\/mrow><\/mfrac>)<\/mo><\/mrow><\/mrow>\\nabla u = \\left( \\frac{\\partial u}{\\partial x},\\ \\frac{\\partial u}{\\partial y},\\ \\frac{\\partial u}{\\partial z} \\right)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

      \u751f\u6d3b\/\u751f\u4ea7\u4f8b\u5b50<\/h3>\n\n\n\n
        \n
      • \u51ac\u5929\u7a97\u6237\uff1a\u70ed\u91cf\u6cbf\u7740\u6e29\u5ea6\u68af\u5ea6<\/strong>\u5f80\u5916\u8dd1<\/li>\n\n\n\n
      • \u7535\u6d41\uff1a\u6cbf\u7740\u7535\u52bf\u68af\u5ea6<\/strong>\u6d41\u52a8<\/li>\n\n\n\n
      • \u6c34\u6d41\uff1a\u6cbf\u7740\u538b\u529b\u68af\u5ea6<\/strong>\u6d41\u52a8<\/li>\n<\/ul>\n\n\n\n
        \n

        \u6ca1\u6709\u68af\u5ea6\uff0c\u5c31\u6ca1\u6709\u4f20\u70ed\u3001\u6ca1\u6709\u7535\u6d41\u3001\u6ca1\u6709\u6d41\u52a8\u3002<\/p>\n<\/blockquote>\n\n\n\n

        COMSOL\u5b98\u65b9\u6848\u4f8b\uff1a\u78c1\u573a\u68af\u5ea6\uff08\u7c92\u5b50 \/ MRI \/ \u78c1\u60ac\u6d6e\uff09<\/h3>\n\n\n\n
          \n
        • \u7528\u9014\uff1a\u7c92\u5b50\u504f\u8f6c\u3001\u78c1\u60ac\u6d6e\u3001MRI\u78c1\u573a\u5747\u5300\u6027\u5206\u6790<\/li>\n\n\n\n
        • \u6838\u5fc3\uff1a\u68af\u5ea6\u8d8a\u5927\uff0c\u573a\u53d8\u5316\u8d8a\u5267\u70c8\uff0c\u53d7\u529b\/\u6548\u5e94\u8d8a\u5f3a<\/strong><\/li>\n<\/ul>\n\n\n\n
          \n\n\n\n

          3\uff09\u6563\u5ea6 Divergence \u2207\u22c5F<\/h1>\n\n\n\n

          \u4e00\u53e5\u8bdd\u7406\u89e3<\/h3>\n\n\n\n

          \u5411\u91cf\u573a\u5728\u8fd9\u91cc\u662f\u201c\u55b7\u6cc9\u201d\u8fd8\u662f\u201c\u5438\u5c18\u5668\u201d\u3002<\/strong><\/p>\n\n\n\n

          \u6563\u5ea6 = \u6e90 \/ \u6c47 \/ \u5b88\u6052\u3002<\/p>\n\n\n\n

          \u6807\u51c6\u516c\u5f0f<\/h3>\n\n\n\n

          \u2207<\/mi>\u22c5<\/mo>F<\/mi>=<\/mo>\u2202<\/mi>F<\/mi>x<\/mi><\/msub><\/mrow>\u2202<\/mi>x<\/mi><\/mrow><\/mfrac>+<\/mo>\u2202<\/mi>F<\/mi>y<\/mi><\/msub><\/mrow>\u2202<\/mi>y<\/mi><\/mrow><\/mfrac>+<\/mo>\u2202<\/mi>F<\/mi>z<\/mi><\/msub><\/mrow>\u2202<\/mi>z<\/mi><\/mrow><\/mfrac><\/mrow>\\nabla\\cdot \\mathbf{F} = \\frac{\\partial F_x}{\\partial x} + \\frac{\\partial F_y}{\\partial y} + \\frac{\\partial F_z}{\\partial z}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

          \u751f\u6d3b\/\u751f\u4ea7\u4f8b\u5b50<\/h3>\n\n\n\n
            \n
          • \u5439\u98ce\u673a\u51fa\u98ce\u53e3\uff1a\u6563\u5ea6 > 0\uff08\u6e90\uff09<\/li>\n\n\n\n
          • \u5438\u5c18\u5668\u8fdb\u98ce\u53e3\uff1a\u6563\u5ea6 < 0\uff08\u6c47\uff09<\/li>\n\n\n\n
          • \u6c34\u7ba1\u4e2d\u95f4\u4e00\u6bb5\uff1a\u4e0d\u589e\u4e0d\u51cf \u2192 \u6563\u5ea6 = 0<\/strong><\/li>\n<\/ul>\n\n\n\n

            \u5de5\u7a0b\u6838\u5fc3\u65b9\u7a0b<\/h3>\n\n\n\n

            \u4e0d\u53ef\u538b\u7f29\u6d41\u4f53\uff08\u6c34\u3001\u6cb9\u3001\u4f4e\u901f\u98ce\uff09\uff1a\u2207<\/mi>\u22c5<\/mo>u<\/mi>=<\/mo>0<\/mn><\/mrow>\\nabla\\cdot \\mathbf{u} = 0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

            \u8fd9\u5c31\u662fCFD\u91cc\u6700\u6838\u5fc3\u7684\u8d28\u91cf\u5b88\u6052<\/strong>\u3002<\/p>\n\n\n\n

            COMSOL\u5b98\u65b9\u6848\u4f8b\uff1a\u540e\u53f0\u9636\u6d41\u52a8\uff08\u6c7d\u8f66\u5c3e\u6d41 \/ \u98ce\u9053\uff09<\/h3>\n\n\n\n
              \n
            • \u5178\u578bCFD\u57fa\u51c6\u7b97\u4f8b<\/li>\n\n\n\n
            • \u6838\u5fc3\u7ea6\u675f\uff1a\u901f\u5ea6\u6563\u5ea6=0\uff0c\u4fdd\u8bc1\u6d41\u4f53\u4f53\u79ef\u5b88\u6052<\/li>\n<\/ul>\n\n\n\n
              \n\n\n\n

              4\uff09\u65cb\u5ea6 Curl \u2207\u00d7F<\/h1>\n\n\n\n

              \u4e00\u53e5\u8bdd\u7406\u89e3<\/h3>\n\n\n\n

              \u573a\u5728\u8fd9\u91cc\u201c\u8f6c\u4e0d\u8f6c\u201d\u3001\u201c\u6da1\u4e0d\u6da1\u201d\u3002<\/strong><\/p>\n\n\n\n

              \u6807\u51c6\u516c\u5f0f<\/h3>\n\n\n\n

              \u2207<\/mi>\u00d7<\/mo>F<\/mi>=<\/mo>\u2223<\/mo>e<\/mi>x<\/mi><\/msub><\/mstyle><\/mtd>e<\/mi>y<\/mi><\/msub><\/mstyle><\/mtd>e<\/mi>z<\/mi><\/msub><\/mstyle><\/mtd><\/mtr>\u2202<\/mi>\u2202<\/mi>x<\/mi><\/mrow><\/mfrac><\/mstyle><\/mtd>\u2202<\/mi>\u2202<\/mi>y<\/mi><\/mrow><\/mfrac><\/mstyle><\/mtd>\u2202<\/mi>\u2202<\/mi>z<\/mi><\/mrow><\/mfrac><\/mstyle><\/mtd><\/mtr>F<\/mi>x<\/mi><\/msub><\/mstyle><\/mtd>F<\/mi>y<\/mi><\/msub><\/mstyle><\/mtd>F<\/mi>z<\/mi><\/msub><\/mstyle><\/mtd><\/mtr><\/mtable>\u2223<\/mo><\/mrow><\/mrow>\\nabla\\times \\mathbf{F} = \\begin{vmatrix} \\mathbf{e}_x & \\mathbf{e}_y & \\mathbf{e}_z \\\\ \\frac{\\partial}{\\partial x} & \\frac{\\partial}{\\partial y} & \\frac{\\partial}{\\partial z} \\\\ F_x & F_y & F_z \\end{vmatrix}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

              \u5c55\u5f00\u5206\u91cf\u5f62\u5f0f\uff1a(<\/mo>\u2202<\/mi>F<\/mi>z<\/mi><\/msub><\/mrow>\u2202<\/mi>y<\/mi><\/mrow><\/mfrac>\u2212<\/mo>\u2202<\/mi>F<\/mi>y<\/mi><\/msub><\/mrow>\u2202<\/mi>z<\/mi><\/mrow><\/mfrac>,<\/mo> <\/mtext>\u2202<\/mi>F<\/mi>x<\/mi><\/msub><\/mrow>\u2202<\/mi>z<\/mi><\/mrow><\/mfrac>\u2212<\/mo>\u2202<\/mi>F<\/mi>z<\/mi><\/msub><\/mrow>\u2202<\/mi>x<\/mi><\/mrow><\/mfrac>,<\/mo> <\/mtext>\u2202<\/mi>F<\/mi>y<\/mi><\/msub><\/mrow>\u2202<\/mi>x<\/mi><\/mrow><\/mfrac>\u2212<\/mo>\u2202<\/mi>F<\/mi>x<\/mi><\/msub><\/mrow>\u2202<\/mi>y<\/mi><\/mrow><\/mfrac>)<\/mo><\/mrow>\\left( \\frac{\\partial F_z}{\\partial y}-\\frac{\\partial F_y}{\\partial z},\\ \\frac{\\partial F_x}{\\partial z}-\\frac{\\partial F_z}{\\partial x},\\ \\frac{\\partial F_y}{\\partial x}-\\frac{\\partial F_x}{\\partial y} \\right)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

              \u751f\u6d3b\/\u751f\u4ea7\u4f8b\u5b50<\/h3>\n\n\n\n
                \n
              • \u9a6c\u6876\u653e\u6c34\u3001\u53f0\u98ce\u3001\u5496\u5561\u6405\u62cc\uff1a\u65cb\u5ea6\u22600<\/li>\n\n\n\n
              • \u9759\u7535\u573a\u3001\u91cd\u529b\u573a\uff1a\u76f4\u7ebf\u6307\u5411\uff0c\u4e0d\u65cb\u8f6c \u2192 \u65cb\u5ea6=0<\/li>\n<\/ul>\n\n\n\n

                \u5de5\u7a0b\u6700\u7ecf\u5178\uff1a\u7535\u78c1\u7089 \/ \u611f\u5e94\u52a0\u70ed<\/h3>\n\n\n\n

                \u6cd5\u62c9\u7b2c\u7535\u78c1\u611f\u5e94\u5b9a\u5f8b\uff08\u5168\u9760\u65cb\u5ea6\u5403\u996d\uff09\uff1a\u2207<\/mi>\u00d7<\/mo>E<\/mi>=<\/mo>\u2212<\/mo>\u2202<\/mi>B<\/mi><\/mrow>\u2202<\/mi>t<\/mi><\/mrow><\/mfrac><\/mrow>\\nabla\\times \\mathbf{E} = -\\frac{\\partial \\mathbf{B}}{\\partial t}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

                \u4ea4\u53d8\u78c1\u573a \u2192 \u7535\u573a\u65cb\u5ea6\u22600 \u2192 \u91d1\u5c5e\u5185\u90e8\u4ea7\u751f\u6da1\u6d41 \u2192 \u53d1\u70ed<\/p>\n\n\n\n

                COMSOL\u5b98\u65b9\u6848\u4f8b\uff1a\u611f\u5e94\u52a0\u70ed\uff08\u91d1\u5c5e\u7194\u70bc \/ \u6dec\u706b\uff09<\/h3>\n\n\n\n
                  \n
                • \u5de5\u4e1a\u70ed\u5904\u7406\u3001\u710a\u63a5\u3001\u7194\u70bc\u6838\u5fc3\u6a21\u578b<\/li>\n\n\n\n
                • \u76f4\u63a5\u6c42\u89e3\u65cb\u5ea6\u65b9\u7a0b<\/li>\n<\/ul>\n\n\n\n
                  \n\n\n\n

                  5\uff09\u62c9\u666e\u62c9\u65af\u7b97\u5b50 Laplacian \u0394u=\u22072u<\/h1>\n\n\n\n

                  \u4e00\u53e5\u8bdd\u7406\u89e3<\/h3>\n\n\n\n

                  \u63cf\u8ff0\u573a\u7684\u201c\u51f9\u51f8\/\u5f2f\u66f2\u7a0b\u5ea6\u201d\uff0c\u8d1f\u8d23\u8ba9\u573a\u53d8\u5e73\u7a33\u3001\u8fbe\u5230\u5e73\u8861\u3002<\/strong><\/p>\n\n\n\n

                  \u6807\u51c6\u516c\u5f0f<\/h3>\n\n\n\n

                  \u0394<\/mi>u<\/mi>=<\/mo>\u2207<\/mi>\u22c5<\/mo>(<\/mo>\u2207<\/mi>u<\/mi>)<\/mo>=<\/mo>\u2202<\/mi>2<\/mn><\/msup>u<\/mi><\/mrow>\u2202<\/mi>x<\/mi>2<\/mn><\/msup><\/mrow><\/mfrac>+<\/mo>\u2202<\/mi>2<\/mn><\/msup>u<\/mi><\/mrow>\u2202<\/mi>y<\/mi>2<\/mn><\/msup><\/mrow><\/mfrac>+<\/mo>\u2202<\/mi>2<\/mn><\/msup>u<\/mi><\/mrow>\u2202<\/mi>z<\/mi>2<\/mn><\/msup><\/mrow><\/mfrac><\/mrow>\\Delta u = \\nabla\\cdot(\\nabla u) = \\frac{\\partial^2 u}{\\partial x^2} + \\frac{\\partial^2 u}{\\partial y^2} + \\frac{\\partial^2 u}{\\partial z^2}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

                  \u751f\u6d3b\/\u751f\u4ea7\u4f8b\u5b50<\/h3>\n\n\n\n
                    \n
                  • \u4e00\u676f\u70ed\u6c34\u653e\u51c9\uff0c\u6700\u540e\u6e29\u5ea6\u5747\u5300\uff1a\u8d8b\u5411 \u0394T=0<\/li>\n\n\n\n
                  • \u623f\u95f4\u6052\u6e29\u3001\u9759\u7535\u5e73\u8861\u3001\u7ed3\u6784\u9759\u529b\u53d8\u5f62\u7a33\u5b9a\uff1a\u90fd\u6ee1\u8db3\u62c9\u666e\u62c9\u65af\u7c7b\u65b9\u7a0b<\/li>\n<\/ul>\n\n\n\n

                    \u5de5\u7a0b\u6700\u5e38\u7528\u65b9\u7a0b<\/h3>\n\n\n\n
                      \n
                    • \u62c9\u666e\u62c9\u65af\u65b9\u7a0b\uff08\u65e0\u6e90\u3001\u7a33\u6001\u3001\u5e73\u8861\uff09\uff1a<\/li>\n<\/ul>\n\n\n\n

                      \u0394<\/mi>u<\/mi>=<\/mo>0<\/mn><\/mrow>\\Delta u = 0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n
                        \n
                      • \u6cca\u677e\u65b9\u7a0b\uff08\u6709\u6e90\u3001\u6709\u70ed\u6e90\/\u7535\u8377\/\u8f7d\u8377\uff09\uff1a<\/li>\n<\/ul>\n\n\n\n

                        \u0394<\/mi>u<\/mi>=<\/mo>f<\/mi><\/mrow>\\Delta u = f<\/annotation><\/semantics><\/math><\/p>\n\n\n\n

                        \u8986\u76d6\u51e0\u4e4e\u6240\u6709\u9759\u573a\/\u7a33\u6001\u95ee\u9898\uff1a<\/p>\n\n\n\n

                        \u7a33\u6001\u70ed\u4f20\u5bfc\u3001\u9759\u7535\u573a\u3001\u5730\u4e0b\u6c34\u6e17\u6d41\u3001\u7ed3\u6784\u9759\u529b\u3001\u7269\u8d28\u6269\u6563<\/strong><\/p>\n\n\n\n

                        COMSOL\u5b98\u65b9\u6848\u4f8b\uff1a\u70b9\u6e90\u6cca\u677e\u65b9\u7a0b\uff08\u70b9\u70ed\u6e90 \/ \u70b9\u7535\u8377 \/ \u96c6\u4e2d\u529b\uff09<\/h3>\n\n\n\n
                          \n
                        • \u82af\u7247\u70ed\u70b9\u3001\u9488\u72b6\u7535\u6781\u3001\u96c6\u4e2d\u8f7d\u8377\u3001\u88c2\u7eb9\u5c16\u7aef<\/li>\n\n\n\n
                        • \u6700\u7ecf\u5178\u7684\u201c\u573a\u7684\u5e73\u8861\u4e0e\u6269\u6563\u201d\u6a21\u578b<\/li>\n<\/ul>\n\n\n\n
                          \n\n\n\n

                          6\uff09\u4e00\u5f20\u8868\u5f7b\u5e95\u5206\u6e05\uff1a5\u4e2a\u6838\u5fc3\u7b97\u5b50\u5bf9\u6bd4<\/h1>\n\n\n\n
                          \u540d\u79f0<\/th>\u6570\u5b66\u7b26\u53f7<\/th>\u6838\u5fc3\u516c\u5f0f\u7b80\u8bb0<\/th>\u4f5c\u7528\u5bf9\u8c61<\/th>\u8f93\u51fa<\/th>\u4eba\u8bdd\u6838\u5fc3<\/th><\/tr><\/thead>
                          \u504f\u5bfc\u6570<\/td>\u2202<\/mi>u<\/mi><\/mrow>\u2202<\/mi>x<\/mi><\/mrow><\/mfrac><\/mstyle><\/mrow>\\dfrac{\\partial u}{\\partial x}<\/annotation><\/semantics><\/math>\u2202x\u2202u\u200b<\/td>\u5355\u65b9\u5411\u6c42\u5bfc<\/td>\u6807\u91cf<\/td>\u6807\u91cf<\/td>\u67d0\u65b9\u5411\u53d8\u5316\u5feb\u6162<\/td><\/tr>
                          \u68af\u5ea6<\/td>\u2207<\/mi>u<\/mi><\/mrow>\\nabla u<\/annotation><\/semantics><\/math>\u2207u<\/td>(<\/mo>\u2202<\/mi>x<\/mi><\/msub>,<\/mo>\u2202<\/mi>y<\/mi><\/msub>,<\/mo>\u2202<\/mi>z<\/mi><\/msub>)<\/mo>u<\/mi><\/mrow>(\\partial_x,\\partial_y,\\partial_z)u<\/annotation><\/semantics><\/math>(\u2202x\u200b,\u2202y\u200b,\u2202z\u200b)u<\/td>\u6807\u91cf<\/td>\u5411\u91cf<\/td>\u6700\u9661\u65b9\u5411\u3001\u9a71\u52a8\u529b<\/td><\/tr>
                          \u6563\u5ea6<\/td>\u2207<\/mi>\u22c5<\/mo>F<\/mi><\/mrow>\\nabla\\cdot\\mathbf{F}<\/annotation><\/semantics><\/math>\u2207\u22c5F<\/td>\u2202<\/mi>x<\/mi><\/msub>F<\/mi>x<\/mi><\/msub>+<\/mo>\u2202<\/mi>y<\/mi><\/msub>F<\/mi>y<\/mi><\/msub>+<\/mo>\u2202<\/mi>z<\/mi><\/msub>F<\/mi>z<\/mi><\/msub><\/mrow>\\partial_x F_x+\\partial_y F_y+\\partial_z F_z<\/annotation><\/semantics><\/math>\u2202x\u200bFx\u200b+\u2202y\u200bFy\u200b+\u2202z\u200bFz\u200b<\/td>\u5411\u91cf<\/td>\u6807\u91cf<\/td>\u6e90\/\u6c47\u3001\u5b88\u6052<\/td><\/tr>
                          \u65cb\u5ea6<\/td>\u2207<\/mi>\u00d7<\/mo>F<\/mi><\/mrow>\\nabla\\times\\mathbf{F}<\/annotation><\/semantics><\/math>\u2207\u00d7F<\/td>\u53c9\u4e58\u884c\u5217\u5f0f<\/td>\u5411\u91cf<\/td>\u5411\u91cf<\/td>\u65cb\u8f6c\u3001\u6da1\u6d41<\/td><\/tr>
                          \u62c9\u666e\u62c9\u65af<\/td>\u0394<\/mi>u<\/mi>=<\/mo>\u2207<\/mi>2<\/mn><\/msup>u<\/mi><\/mrow>\\Delta u=\\nabla^2 u<\/annotation><\/semantics><\/math>\u0394u=\u22072u<\/td>\u2202<\/mi>x<\/mi>2<\/mn><\/msubsup>+<\/mo>\u2202<\/mi>y<\/mi>2<\/mn><\/msubsup>+<\/mo>\u2202<\/mi>z<\/mi>2<\/mn><\/msubsup><\/mrow>\\partial_x^2+\\partial_y^2+\\partial_z^2<\/annotation><\/semantics><\/math>\u2202x2\u200b+\u2202y2\u200b+\u2202z2\u200b<\/td>\u6807\u91cf<\/td>\u6807\u91cf<\/td>\u5e73\u8861\u3001\u6269\u6563\u3001\u7a33\u6001<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
                          \n
                          \"\"<\/figure>\n<\/figure>\n\n\n\n

                          7\uff09\u4eff\u771f\u5de5\u7a0b\u5e08\u6700\u8be5\u8bb0\u4f4f\u76844\u53e5\u7269\u7406<\/h1>\n\n\n\n
                            \n
                          1. \u68af\u5ea6\u8d1f\u8d23\u201c\u9a71\u52a8\u201d<\/strong>\uff1a\u6e29\u5dee\u3001\u7535\u52bf\u5dee\u3001\u538b\u529b\u5dee \u2192 \u63a8\u52a8\u4e00\u5207\u6d41\u52a8\u4e0e\u4f20\u9012<\/li>\n\n\n\n
                          2. \u6563\u5ea6\u8d1f\u8d23\u201c\u5b88\u6052\u201d<\/strong>\uff1a\u6d41\u4f53\u4e0d\u589e\u4e0d\u51cf\u3001\u7535\u8377\u5b88\u6052\u3001\u8d28\u91cf\u5b88\u6052<\/li>\n\n\n\n
                          3. \u65cb\u5ea6\u8d1f\u8d23\u201c\u65cb\u8f6c\u4e0e\u611f\u5e94\u201d<\/strong>\uff1a\u6da1\u6d41\u3001\u7535\u673a\u3001\u611f\u5e94\u52a0\u70ed\u5168\u9760\u5b83<\/li>\n\n\n\n
                          4. \u62c9\u666e\u62c9\u65af\u8d1f\u8d23\u201c\u5e73\u8861\u4e0e\u7a33\u6001\u201d<\/strong>\uff1a\u9759\u573a\u3001\u7a33\u6001\u3001\u6269\u6563\u95ee\u9898\u7684\u6838\u5fc3\u9aa8\u67b6<\/li>\n<\/ol>\n\n\n\n

                            \u4f60\u5728 COMSOL \u91cc\u9009\u7684\u6bcf\u4e00\u4e2a\u7269\u7406\u573a\u63a5\u53e3\uff1a<\/p>\n\n\n\n

                            \u4f20\u70ed\u3001CFD\u3001\u9759\u7535\u3001\u78c1\u573a\u3001\u7ed3\u6784\u3001\u6269\u6563<\/strong><\/p>\n\n\n\n

                            \u80cc\u540e\u90fd\u662f\u8fd9\u4e94\u4e2a\u7b97\u5b50\u5728\u652f\u6491\u3002<\/p>\n\n\n\n

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

                            \uff08\u6709\u8da3\u4e0d\u6666\u6da9\u3001\u516c\u5f0f\u4e0d\u5413\u4eba\u3001\u770b\u5b8c\u80fd\u5206\u6e05\u3001\u5efa\u6a21\u7528\u5f97\u4e0a\uff09 \u505a\u6709\u9650\u5143\u3001\u505a\u591a\u7269\u7406\u573a\u8026\u5408\uff0c\u504f\u5bfc\u3001\u68af\u5ea6\u3001\u6563\u5ea6\u3001\u65cb\u5ea6\u3001\u62c9\u666e\u62c9\u65af […]<\/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-1159","post","type-post","status-publish","format-standard","hentry","category-comsol"],"_links":{"self":[{"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=\/wp\/v2\/posts\/1159","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=1159"}],"version-history":[{"count":5,"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=\/wp\/v2\/posts\/1159\/revisions"}],"predecessor-version":[{"id":1166,"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=\/wp\/v2\/posts\/1159\/revisions\/1166"}],"wp:attachment":[{"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1159"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1159"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/guagefangzhen.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1159"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}