| 基于变分原理的三维扩散方程离散化格式 |
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| 引用本文： | 陈光南,李德元,万正苏.基于变分原理的三维扩散方程离散化格式[J].计算物理,2003,20(4):291-297. |
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| 作者姓名： | 陈光南 李德元 万正苏 |
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| 作者单位： | 1. 北京虚用物理与计算数学研究所 计算物理实验室, 100088;2. 上海大学数学系, 上海 200436 |
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| 基金项目： | 国家高技术863计划惯性约束聚变委员会和计算物理国家重点实验室基金资助项目 |
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| 摘 要： | 研究三维扩散方程的数值模拟.在非正规六面体网格上,用变分原理建立扩散流形式的差分格式.将扩散流通量作为未知函数,求其泛函极值,并与原函数温度联立求解.详细推导了计算公式,并给出了数值试验结果.
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| 关 键 词： | 变分原理 非正规六面体网格 三维扩散方程 差分格式 |
| 文章编号： | 1001-246X(2003)04-0291-07 |
| 收稿时间： | 2002-03-27 |
| 修稿时间： | 2002年3月27日 |
Discrete Scheme Based on Variation Principle for Three Dimensional Diffusion Equation |
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| CHEN Guang-nan,LI De-yuan,WAN Zheng-su.Discrete Scheme Based on Variation Principle for Three Dimensional Diffusion Equation[J].Chinese Journal of Computational Physics,2003,20(4):291-297. |
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| Authors: | CHEN Guang-nan LI De-yuan WAN Zheng-su |
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| Institution: | 1. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;2. Department of Mathematics, Shanghai University, Shanghai 200436, China |
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| Abstract: | Numerical simulation for three dimensional diffusion equation is studied.Using variation principle,the difference discrete scheme with diffusion flux form on the irregular hexahedral grid is constructed.The flux of diffusion as an unknown function is obtained by minimizing the functional and solved with the equation of temperature function simultaneously.Computational formulas are deduced and numerical test is given. |
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| Keywords: | variation principle irregular hexahedral grid three-dimensional diffusion equation difference scheme |
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