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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (2): 213-225.doi: 10.3969/j.issn.1005-3085.2015.02.006

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求解椭圆型方程界面问题的修正有限体积方法

续小磊,   冯秀芳   

  1. 宁夏大学数学与计算机学院，银川 750021
  • 收稿日期:2013-04-28 接受日期:2014-04-18 出版日期:2015-04-15 发布日期:2015-06-15
  • 基金资助:
    国家自然科学基金 (11161036; 11361045)；宁夏自然科学基金 (NZ14233).

A Modified Finite Volume Method for Solving Interface Problem of Elliptic Equation

XU Xiao-lei,   FENG Xiu-fang   

  1. School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021
  • Received:2013-04-28 Accepted:2014-04-18 Online:2015-04-15 Published:2015-06-15
  • Supported by:
    The National Natural Science Foundation of China (11161036; 11361045); the Natural Science Foundation of Ningxia (NZ14233).

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摘要： 本文基于经典的有限体积方法，讨论了带有间断系数二维椭圆型方程的求解问题．文中通过在求解椭圆型方程时截取通量函数的更多项泰勒展开式，同时结合有限差分方法对与边界相邻的网格点进行特殊处理，改进了间断系数的求解方法，得到了一种修正的有限体积方法，该方法在界面处是一阶精度，但方法整体可达到二阶精度．数值实验表明，文中构造的修正有限体积方法是有效的．

关键词: 椭圆型方程, 有限体积方法, 界面问题, 调和平均法

Abstract:

Based on classical finite volume method for solving two dimensional elliptic equation with discontinuous efficient, a modified finite volume method is presented in this paper. The finite difference method is cooperated with for dealing with some grid point around boundary, and more Taylor expansion items of flux function are intercepted in order to obtain higher numerical accuracy. There is first order accuracy at interface and second order accuracy in the whole domain. Numerical results indicate that the modified finite volume method is effective.

Key words: elliptic equation, finite volume method, interface problem, harmonic averaging method

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