| 基于变分原理的二维热传导方程差分格式 |
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| 引用本文： | 陈光南,张永慧.基于变分原理的二维热传导方程差分格式[J].计算物理,2002,19(4):299-304. |
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| 作者姓名： | 陈光南 张永慧 |
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| 作者单位： | 北京应用物理与计算数学研究所, 北京 100088 |
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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中国工程物理研究院科学技术基金资助项目 |
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| 摘 要： | 研究二维热传导方程的差分数值模拟.用变分原理在不规则结构网格上建立热流通量形式的差分格式.将热流通量作为未知函数求泛函极值,并与温度函数联立求解.克服通常九点格式用插值方法计算网格边界上的热传导系数和网格结点上的温度所引入的误差.
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| 关 键 词： | 变分原理 二维热传导方程 不规则结构网格 |
| 文章编号： | 1001-246X(2002)04-0299-06 |
| 收稿时间： | 2001-01-03 |
| 修稿时间： | 2001年1月3日 |
DIFFERENCE SCHEME BASED ON VARIATIONAL PRINCIPLE FOR TWO DIMENSIONAL THERMAL CONDUCTION EQUATION |
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| CHEN Guang-nan,ZHANG Yong-hui.DIFFERENCE SCHEME BASED ON VARIATIONAL PRINCIPLE FOR TWO DIMENSIONAL THERMAL CONDUCTION EQUATION[J].Chinese Journal of Computational Physics,2002,19(4):299-304. |
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| Authors: | CHEN Guang-nan ZHANG Yong-hui |
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| Institution: | Institute of Applied Physics and Computational Mathematics, Beijing 100088, China |
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| Abstract: | Difference numerical simulation for two dimensional thermal conduction equation is studied.Using the variational principle,the difference scheme with thermal-flux form in the irregular structured mesh is presented.The thermal flux as an unknown function is obtained by minimizing the functional and solved with the equation of temperature function simultaneously.This scheme overcomes the defects of general nine-point schemes,which have to calculate the thermal conduction coefficients on the cell boundaries and the temperatures located in the cell vertices by interpolation. |
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| Keywords: | variational principle two dimensional thermal conduction equation irregular structured mesh |
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