{"id":1511,"date":"2021-10-10T12:24:02","date_gmt":"2021-10-10T03:24:02","guid":{"rendered":"http:\/\/www.miyamoto-lab.com\/?p=1511"},"modified":"2021-10-10T13:44:18","modified_gmt":"2021-10-10T04:44:18","slug":"sfd8gsdfgij","status":"publish","type":"post","link":"https:\/\/www.miyamoto-lab.com\/ja\/2021\/10\/10\/sfd8gsdfgij\/","title":{"rendered":"9. \u79fb\u6d41\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u3055\u3066\u3044\u3088\u3044\u3088\u79fb\u6d41\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u3092\u8003\u3048\u3088\u3046\u3002\u4ee5\u4e0b\u3067\u306f\u7c21\u5358\u306e\u305f\u3081\u30011\u6b21\u5143\u306e\u79fb\u6d41\u65b9\u7a0b\u5f0f<\/p>\n\n\n\n<figure class=\"wp-block-image\" id=\"block-b2efb3c3-b2c1-47b7-9051-24968d36f9b9\"><img decoding=\"async\" src=\"http:\/\/www.miyamoto-lab.com\/wp-content\/uploads\/2020\/10\/advection.jpg\" alt=\"\u753b\u50cf\u306b alt \u5c5e\u6027\u304c\u6307\u5b9a\u3055\u308c\u3066\u3044\u307e\u305b\u3093\u3002\u30d5\u30a1\u30a4\u30eb\u540d: advection.jpg\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"block-c40606b3-d5e5-4de9-9b4a-20b6a9af8728\">$$\\frac{\\partial T}{\\partial t}+u\\frac{\\partial T}{\\partial x}=0$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"block-3428589b-1f61-4a3c-afa5-0354b408d2c3\">\u3092\u89e3\u304f\u3053\u3068\u3092\u8003\u3048\u308b\u3002\u3053\u308c\u306f\u901f\u5ea6$u$\u3067\u4f55\u3089\u304b\u306e\u7269\u7406\u91cf$T$\u3092\u5f62\u3092\u5909\u3048\u305a\u306b\u904b\u3093\u3067\u3044\u308b\u3053\u3068\u306b\u76f8\u5f53\u3059\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"block-b9e0e411-0d28-49ec-b28a-595fd313cc9b\">\u3053\u308c\u306f\u308f\u3056\u308f\u3056\u6570\u5024\u8a08\u7b97\u306a\u3069\u3067\u89e3\u304f\u307e\u3067\u3082\u306a\u304f\u3001\u53f3\uff08$x$\u306b\u3064\u3044\u3066\u30d7\u30e9\u30b9\u5074\u306b\u52d5\u304f\u3082\u306e\u306f$T(x,t)=f(x-ut)$\u3068\u3044\u3046\u4e00\u822c\u89e3\u3092\u6301\u3064\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"block-e7d17c11-e907-48b4-9223-985ad609c9b1\">\u3055\u3066\u554f\u984c\u306f\u3001\u3053\u308c\u3092\u3069\u306e\u3088\u3046\u306b\u3057\u3066\u6570\u5024\u7684\u306b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u304b\u3001\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002\u3053\u308c\u3092\u5dee\u5206\u5f62\u5f0f\u3067\u66f8\u3044\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"block-dfb73d2c-9f47-4553-89e9-02c65ddece3b\">$$\\frac{T_i^{n+1}-T_i^{n}}{\\Delta t}=-u\\frac{T_{i+1}^n-T_i^n}{\\Delta x}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"block-b61595ba-8816-418e-ae21-64005ce89f5a\">$$T_i^{n+1}=T_i^{n}-u\\frac{\\Delta t}{\\Delta x}(T_{i+1}^n-T_i^n)$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" id=\"block-17d769c1-73b0-4293-a8ed-1eda10e8de9e\">\u3068\u8003\u3048\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u307e\u305a\u3053\u308c\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u3053\u3068\u306b\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u5dee\u5206\u5f62\u5f0f\u3067\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u3092\u4f5c\u6210\u3057\u3066\u307f\u3088\u3046<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7df4\u7fd2\u554f\u984c9-1.<\/p>\n\n\n\n<div class=\"hcb_wrap\"><pre class=\"prism line-numbers lang-c\" data-lang=\"C\"><code>#include &lt;stdio.h&gt;\n#include &lt;math.h&gt;\n#define u 1.0\n#define dt 0.1\n#define xmax 200\n#define imax 200\n#define tmax 10\n\nint main(void){\n  double dx=(double)xmax\/imax;\n  double x;\n  double T[xmax+1],cfl;\n  int t;\n  cfl=u*dt\/dx;\n  int i;\n  for (i=1; i&lt;=imax; i++){\n    if (i&gt;=10&&i&lt;50)\n      T[i]=1.0;\n    else\n      T[i]=0.0;\n  }\n  for (i=1; i&lt;imax; i++)\n    printf(&quot;%2.2e,&quot;,T[i]);\n  printf(&quot;\\n&quot;);   \n  for (t=1; t&lt;=tmax; t++){\n    for (i=1; i&lt;imax; i++)\n      T[i]=\u3053\u3053\u306b\u8a18\u8ff0\u3059\u308b;\n    if (t%1==0){\n      for (i=1; i&lt;imax; i++)\n        printf(&quot;%2.2e,&quot;,T[i]);\n      printf(&quot;\\n&quot;);\n    }\n  }  \n}<\/code><\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u308c\u306f\u3001\u5b9f\u306f\u6570\u5024\u7684\u306b\u767a\u6563\u3057\u3066\u3057\u307e\u3046\u3053\u3068\u3092\u78ba\u304b\u3081\u308b\u305f\u3081\u306e\u30b3\u30fc\u30c9\u306b\u306a\u3063\u3066\u3044\u308b\u3002\u3053\u308c\u3067\u306f\u6570\u5024\u7684\u306b\u767a\u6563\u3057\u3066\u3057\u307e\u3046\u3053\u3068\u304c\u78ba\u304b\u3081\u3089\u308c\u305f\u3089\u3001\u6b21\u306b\u5dee\u5206\u306e\u65b9\u6cd5\u3092\u3084\u308a\u306a\u304a\u3057\u3066\u307f\u308b\u3002\u307e\u305a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$T_i^{n+1}=T_i^{n}-u\\frac{\\Delta t}{\\Delta x}(T_{i+1}^n-T_i^n)$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u306e\u4ee3\u308f\u308a\u306b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$T_i^{n+1}=T_i^{n}-u\\frac{\\Delta t}{\\Delta x}(T_{i}^n-T_{i-1}^n)$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3068\u3057\u3066\u307f\u3088\u3046\u3002\u8a08\u7b97\u3092100\u30b9\u30c6\u30c3\u30d7\u3054\u3068\u306b\u7d50\u679c\u3092\u66f8\u304d\u3060\u3059\u3088\u3046\u306b\u5909\u66f4\u3057\u3066\u3001\u3055\u3089\u306b\u6642\u9593\u6642\u9593\u309210\u304b\u3089500\u306b\u5909\u66f4\u3057\u3066\u305f\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u3092\u5b8c\u6210\u3057\u3066\u307f\u3088\uff1a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7df4\u7fd2\u554f\u984c9-2.<\/p>\n\n\n\n<div class=\"hcb_wrap\"><pre class=\"prism line-numbers lang-c\" data-lang=\"C\"><code>#include &lt;stdio.h&gt;\n#include &lt;math.h&gt;\n#define u 1.0\n#define dt 0.1\n#define xmax 200\n#define imax 200\n#define tmax 500\n\nint main(void){\n  double dx=(double)xmax\/imax;\n  double x;\n  double T[xmax+1],cfl;\n  int t;\n  cfl=u*dt\/dx;\n  int i;\n  for (i=0; i&lt;=imax; i++){\n    if (i&gt;=10&&i&lt;50)\n      T[i]=1.0;\n    else\n      T[i]=0.0;\n  }\n  for (i=1; i&lt;imax; i++)\n    printf(&quot;%2.2e,&quot;,T[i]);\n  printf(&quot;\\n&quot;);   \n  for (t=1; t&lt;=tmax; t++){\n    for (i=1; i&lt;imax; i++)\n      T[i]=\u3053\u3053\u306b\u8a18\u8ff0\u3059\u308b;\n    if (t%100==0){\n      for (i=1; i&lt;imax; i++)\n        printf(&quot;%2.2e,&quot;,T[i]);\n      printf(&quot;\\n&quot;);\n    }\n  }  \n} <\/code><\/pre><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3055\u3066\u3044\u3088\u3044\u3088\u79fb\u6d41\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u3092\u8003\u3048\u3088\u3046\u3002\u4ee5\u4e0b\u3067\u306f\u7c21\u5358\u306e\u305f\u3081\u30011\u6b21\u5143\u306e\u79fb\u6d41\u65b9\u7a0b\u5f0f $$\\frac{\\partial T}{\\partial t}+u\\frac{\\partial T}{\\partial x}=0$$ \u3092 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_locale":"ja","_original_post":"http:\/\/www.miyamoto-lab.com\/?p=1511","footnotes":""},"categories":[1],"tags":[],"class_list":["post-1511","post","type-post","status-publish","format-standard","hentry","category-uncategorized","ja"],"_links":{"self":[{"href":"https:\/\/www.miyamoto-lab.com\/wp-json\/wp\/v2\/posts\/1511","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.miyamoto-lab.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.miyamoto-lab.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.miyamoto-lab.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.miyamoto-lab.com\/wp-json\/wp\/v2\/comments?post=1511"}],"version-history":[{"count":4,"href":"https:\/\/www.miyamoto-lab.com\/wp-json\/wp\/v2\/posts\/1511\/revisions"}],"predecessor-version":[{"id":1522,"href":"https:\/\/www.miyamoto-lab.com\/wp-json\/wp\/v2\/posts\/1511\/revisions\/1522"}],"wp:attachment":[{"href":"https:\/\/www.miyamoto-lab.com\/wp-json\/wp\/v2\/media?parent=1511"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.miyamoto-lab.com\/wp-json\/wp\/v2\/categories?post=1511"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.miyamoto-lab.com\/wp-json\/wp\/v2\/tags?post=1511"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}