{"id":1669,"date":"2024-12-20T19:00:11","date_gmt":"2024-12-20T11:00:11","guid":{"rendered":"https:\/\/www.mustenaka.cn\/?p=1669"},"modified":"2024-12-25T11:17:23","modified_gmt":"2024-12-25T03:17:23","slug":"sph-formula-summary","status":"publish","type":"post","link":"https:\/\/www.mustenaka.cn\/index.php\/2024\/12\/20\/sph-formula-summary\/","title":{"rendered":"SPH\u516c\u5f0f\u603b\u7ed3"},"content":{"rendered":"

SPH\u516c\u5f0f\u603b\u7ed3<\/span><\/h1>\n

SPH\u57fa\u672c\u516c\u5f0f<\/span><\/h2>\n
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\u52a0\u901f\u5ea6<\/span><\/h2>\n

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\u538b\u529b<\/span><\/h2>\n

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\u7c98\u5ea6<\/span><\/h2>\n

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\u5728\u52a0\u901f\u5ea6\u4e2d\uff0c\u53ef\u4ee5\u6d88\u5143m<\/span><\/p>\n

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\u901f\u5ea6<\/span><\/h2>\n

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\u8fed\u4ee3<\/span><\/h2>\n

1. \u6b27\u62c9\u6cd5\uff08Euler Method\uff09<\/span><\/h3>\n

\u516c\u5f0f\uff1a<\/span><\/strong><\/span><\/p>\n

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\u601d\u60f3\uff1a<\/span><\/strong><\/span> \u6b27\u62c9\u6cd5\u662f\u4e00\u79cd\u663e\u5f0f\u7684\u65b9\u6cd5\uff0c\u5229\u7528\u5f53\u524d\u65f6\u523b\u7684\u901f\u5ea6\u548c\u52a0\u901f\u5ea6\u6765\u9884\u6d4b\u4e0b\u4e00\u4e2a\u65f6\u523b\u7684\u72b6\u6001\u3002\u8fd9\u79cd\u65b9\u6cd5\u7b80\u5355\u76f4\u89c2\uff0c\u4f46\u7cbe\u5ea6\u8f83\u4f4e\u3002<\/span><\/p>\n

\u4f18\u7f3a\u70b9\uff1a<\/span><\/strong><\/span><\/p>\n

    \n
  • \n

    \u4f18\u70b9<\/span><\/strong><\/span>\uff1a\u5b9e\u73b0\u7b80\u5355\uff0c\u8ba1\u7b97\u91cf\u5c0f\uff0c\u9002\u5408\u521d\u5b66\u8005\u548c\u8f83\u7b80\u5355\u7684\u7269\u7406\u7cfb\u7edf\u3002<\/span><\/p>\n<\/li>\n

  • \n

    \u7f3a\u70b9<\/span><\/strong><\/span>\uff1a\u4e0d\u9002\u5408\u9ad8\u7cbe\u5ea6\u6a21\u62df\uff0c\u5c24\u5176\u662f\u5728\u7cfb\u7edf\u4e2d\u6709\u5927\u7684\u52a0\u901f\u5ea6\u53d8\u5316\u65f6\uff0c\u53ef\u80fd\u5bfc\u81f4\u6570\u503c\u4e0d\u7a33\u5b9a\u3002<\/span><\/p>\n<\/li>\n<\/ul>\n

    \n
    \n<\/div>\n

    2. \u9690\u5f0f\u6b27\u62c9\u6cd5\uff08Implicit Euler Method\uff09<\/span><\/h3>\n

    \u516c\u5f0f\uff1a<\/span><\/strong><\/span><\/p>\n

    \u9690\u5f0f\u6b27\u62c9\u6cd5\u7684\u66f4\u65b0\u516c\u5f0f\u5982\u4e0b\uff1a<\/span><\/p>\n

    \n
    \n
    <\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/defs><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/g><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/g><\/g><\/g><\/svg><\/span><\/div>\n<\/div>\n<\/div>\n

    \u601d\u60f3\uff1a<\/span><\/strong><\/span> \u9690\u5f0f\u6b27\u62c9\u6cd5\u662f\u9690\u5f0f\u65b9\u6cd5\uff0c\u901f\u5ea6\u548c\u52a0\u901f\u5ea6\u7684\u66f4\u65b0\u4f9d\u8d56\u4e8e\u4e0b\u4e00\u65f6\u523b\u7684\u72b6\u6001\u3002\u8fd9\u79cd\u65b9\u6cd5\u76f8\u6bd4\u663e\u5f0f\u6b27\u62c9\u6cd5\u66f4\u4e3a\u7a33\u5b9a\uff0c\u5c24\u5176\u5728\u5904\u7406\u521a\u6027\u7269\u4f53\u6216\u5927\u52a0\u901f\u5ea6\u53d8\u5316\u65f6\u5177\u6709\u66f4\u597d\u7684\u6570\u503c\u7a33\u5b9a\u6027\u3002<\/span><\/p>\n

    \u4f18\u7f3a\u70b9\uff1a<\/span><\/strong><\/span><\/p>\n

      \n
    • \n

      \u4f18\u70b9<\/span><\/strong><\/span>\uff1a\u6570\u503c\u7a33\u5b9a\u6027\u597d\uff0c\u9002\u7528\u4e8e\u521a\u6027\u7cfb\u7edf\u3002<\/span><\/p>\n<\/li>\n

    • \n

      \u7f3a\u70b9<\/span><\/strong><\/span>\uff1a\u6bcf\u4e00\u6b65\u9700\u8981\u6c42\u89e3\u4e00\u4e2a\u65b9\u7a0b\uff08\u4f8b\u5982\u6c42\u89e3\u52a0\u901f\u5ea6\uff09\uff0c\u8ba1\u7b97\u91cf\u76f8\u5bf9\u8f83\u5927\uff0c\u4e14\u4e0d\u5bb9\u6613\u5e76\u884c\u5316\u3002<\/span><\/p>\n<\/li>\n<\/ul>\n

      \n
      \n<\/div>\n

      3. \u534a\u9690\u5f0f\u6b27\u62c9\u6cd5\uff08Semi-Implicit Euler Method\uff09<\/span><\/h3>\n

      \u516c\u5f0f\uff1a<\/span><\/strong><\/span><\/p>\n

      \u534a\u9690\u5f0f\u6b27\u62c9\u6cd5\u7ed3\u5408\u4e86\u663e\u5f0f\u548c\u9690\u5f0f\u65b9\u6cd5\u7684\u4f18\u70b9\uff1a<\/span><\/p>\n

      \n
      \n
      <\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/defs><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/g><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/g><\/g><\/svg><\/span><\/div>\n<\/div>\n<\/div>\n

      \u601d\u60f3\uff1a<\/span><\/strong><\/span> \u534a\u9690\u5f0f\u6b27\u62c9\u6cd5\u5728\u5904\u7406\u521a\u6027\u7269\u4f53\u65f6\u8868\u73b0\u826f\u597d\uff0c\u80fd\u591f\u5728\u4e0d\u589e\u52a0\u592a\u591a\u8ba1\u7b97\u8d1f\u62c5\u7684\u60c5\u51b5\u4e0b\uff0c\u6539\u8fdb\u6570\u503c\u7a33\u5b9a\u6027\u3002\u5b83\u5e38\u7528\u4e8e\u7269\u7406\u5f15\u64ce\u4e2d\uff0c\u5c24\u5176\u662f\u5904\u7406\u901f\u5ea6\u548c\u52a0\u901f\u5ea6\u7684\u8026\u5408\u3002<\/span><\/p>\n

      \u4f18\u7f3a\u70b9\uff1a<\/span><\/strong><\/span><\/p>\n

        \n
      • \n

        \u4f18\u70b9<\/span><\/strong><\/span>\uff1a\u76f8\u8f83\u4e8e\u663e\u5f0f\u6b27\u62c9\u6cd5\u5177\u6709\u66f4\u597d\u7684\u7a33\u5b9a\u6027\uff0c\u8ba1\u7b97\u6210\u672c\u4f4e\u3002<\/span><\/p>\n<\/li>\n

      • \n

        \u7f3a\u70b9<\/span><\/strong><\/span>\uff1a\u867d\u7136\u6709\u8f83\u597d\u7684\u7a33\u5b9a\u6027\uff0c\u4f46\u4ecd\u7136\u53ef\u80fd\u5728\u67d0\u4e9b\u7269\u7406\u7cfb\u7edf\u4e2d\u51fa\u73b0\u4e0d\u51c6\u786e\u7684\u7ed3\u679c\uff0c\u7279\u522b\u662f\u5bf9\u4e8e\u8f83\u590d\u6742\u7684\u7cfb\u7edf\u3002<\/span><\/p>\n<\/li>\n<\/ul>\n

        \n
        \n<\/div>\n

        4. Verlet\u79ef\u5206\uff08Verlet Integration\uff09<\/span><\/h3>\n

        \u516c\u5f0f\uff1a<\/span><\/strong><\/span><\/p>\n

        Verlet\u79ef\u5206\u7684\u57fa\u672c\u516c\u5f0f\u5982\u4e0b\uff1a<\/span><\/p>\n

        \n
        \n
        <\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/defs><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/g><\/svg><\/span><\/div>\n<\/div>\n<\/div>\n

        \u8be5\u516c\u5f0f\u6ca1\u6709\u76f4\u63a5\u663e\u5f0f\u8ba1\u7b97\u901f\u5ea6\uff0c\u800c\u662f\u901a\u8fc7\u52a0\u901f\u5ea6\u548c\u4f4d\u7f6e\u66f4\u65b0\u6765\u95f4\u63a5\u8ba1\u7b97\u3002<\/span><\/p>\n

        \u601d\u60f3\uff1a<\/span><\/strong><\/span> Verlet\u79ef\u5206\u662f\u4e00\u79cd\u7ecf\u5178\u7684\u79ef\u5206\u65b9\u6cd5\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u5206\u5b50\u52a8\u529b\u5b66\u548c\u7269\u7406\u5f15\u64ce\u4e2d\u3002\u5b83\u7684\u4f18\u70b9\u662f\u5bf9\u6570\u503c\u7a33\u5b9a\u6027\u8f83\u597d\uff0c\u5e76\u4e14\u80fd\u591f\u907f\u514d\u901f\u5ea6\u7684\u76f4\u63a5\u8ba1\u7b97\uff0c\u56e0\u6b64\u9002\u5408\u9700\u8981\u7cbe\u786e\u4f4d\u7f6e\u53d8\u5316\u7684\u6a21\u62df\u3002<\/span><\/p>\n

        \u4f18\u7f3a\u70b9\uff1a<\/span><\/strong><\/span><\/p>\n

          \n
        • \n

          \u4f18\u70b9<\/span><\/strong><\/span>\uff1a\u5bf9\u80fd\u91cf\u4fdd\u5b58\u8f83\u597d\uff0c\u6570\u503c\u7a33\u5b9a\u6027\u8f83\u5f3a\uff0c\u5c24\u5176\u9002\u7528\u4e8e\u6a21\u62df\u957f\u65f6\u95f4\u5c3a\u5ea6\u7684\u7269\u7406\u7cfb\u7edf\u3002<\/span><\/p>\n<\/li>\n

        • \n

          \u7f3a\u70b9<\/span><\/strong><\/span>\uff1a\u6ca1\u6709\u76f4\u63a5\u8ba1\u7b97\u901f\u5ea6\uff0c\u96be\u4ee5\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u5f97\u5230\u7cbe\u786e\u7684\u901f\u5ea6\u4fe1\u606f\u3002\u8ba1\u7b97\u6210\u672c\u8f83\u9ad8\u3002<\/span><\/p>\n<\/li>\n<\/ul>\n

          \n
          \n<\/div>\n

          5. \u7ecf\u51784\u9636Runge-Kutta\uff08RK4\uff09<\/span><\/h3>\n

          \u516c\u5f0f\uff1a<\/span><\/strong><\/span><\/p>\n

          RK4\u6cd5\u662f\u56db\u9636\u7cbe\u5ea6\u7684Runge-Kutta\u65b9\u6cd5\uff0c\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\uff1a<\/span><\/p>\n

          \n
          \n
          <\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/path><\/defs><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/rect><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/g><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/rect><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/g><\/g><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/rect><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/g><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/rect><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/g><\/g><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/rect><\/path><\/use><\/path><\/use><\/g><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/path><\/use><\/path><\/use><\/g><\/path><\/use><\/g><\/g><\/svg><\/span><\/div>\n<\/div>\n<\/div>\n

          \u5176\u4e2d, f(t_n, x_n) \u662f\u5bf9\u7cfb\u7edf\u72b6\u6001\u7684\u5fae\u5206\uff08etc. \u901f\u5ea6\u3001\u52a0\u901f\u5ea6\uff09<\/span><\/p>\n

          \u601d\u60f3\uff1a<\/span><\/strong><\/span> RK4\u6cd5\u662f\u4e00\u79cd\u663e\u5f0f\u65b9\u6cd5\uff0c\u901a\u8fc7\u5bf9\u7cfb\u7edf\u8fdb\u884c\u56db\u6b21\u4f30\u8ba1\uff0c\u91c7\u7528\u52a0\u6743\u5e73\u5747\u7684\u65b9\u5f0f\u6765\u63d0\u9ad8\u7cbe\u5ea6\u3002\u5b83\u6bd4\u6b27\u62c9\u6cd5\u7b49\u7b80\u5355\u65b9\u6cd5\u5177\u6709\u66f4\u9ad8\u7684\u51c6\u786e\u6027\u3002<\/span><\/p>\n

          \u4f18\u7f3a\u70b9\uff1a<\/span><\/strong><\/span><\/p>\n

            \n
          • \n

            \u4f18\u70b9<\/span><\/strong><\/span>\uff1a\u7cbe\u5ea6\u9ad8\uff0c\u6bd4\u6b27\u62c9\u6cd5\u548c\u9690\u5f0f\u65b9\u6cd5\u6709\u66f4\u597d\u7684\u8868\u73b0\uff0c\u9002\u7528\u4e8e\u5bf9\u7cbe\u5ea6\u8981\u6c42\u8f83\u9ad8\u7684\u7cfb\u7edf\u3002<\/span><\/p>\n<\/li>\n

          • \n

            \u7f3a\u70b9<\/span><\/strong><\/span>\uff1a\u8ba1\u7b97\u5f00\u9500\u8f83\u5927\uff0c\u9700\u8981\u56db\u6b21\u8bc4\u4f30\u51fd\u6570\uff0c\u9002\u7528\u4e8e\u65f6\u95f4\u6b65\u957f\u8f83\u5c0f\u7684\u573a\u666f\uff0c\u4e0d\u9002\u7528\u4e8e\u6781\u5927\u8ba1\u7b97\u91cf\u7684\u5b9e\u65f6\u6a21\u62df\u3002<\/span><\/p>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

            SPH\u516c\u5f0f\u603b\u7ed3 SPH\u57fa\u672c\u516c\u5f0f \u901a\u8fc7\u5dee\u503c\u7684\u65b9\u5f0f\uff0c\u5c06\u6240\u6709\u7684\u7c92\u5b50\u66f4\u65b0\uff0cA\u4e3arj\u5904\u7684\u573a\u91cf\uff0cj\u904d\u5386\u6240\u6709\u7c92\u5b50\uff0c […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[136,137,116],"class_list":["post-1669","post","type-post","status-publish","format-standard","hentry","category-algorithm","tag-physic","tag-sph","tag-unity3d"],"views":1988,"_links":{"self":[{"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/posts\/1669","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/comments?post=1669"}],"version-history":[{"count":3,"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/posts\/1669\/revisions"}],"predecessor-version":[{"id":1673,"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/posts\/1669\/revisions\/1673"}],"wp:attachment":[{"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/media?parent=1669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/categories?post=1669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/tags?post=1669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}