求解带有间断系数泊松方程的修正有限体积

计算机工程与应用 ›› 2013, Vol. 49 ›› Issue (23): 35-38.

求解带有间断系数泊松方程的修正有限体积

续小磊，冯秀芳

宁夏大学数学计算机学院，银川 750021

出版日期:2013-12-01 发布日期:2016-06-12

New modified finite volume approximation of elliptic equations with discontinuous coefficients

XU Xiaolei, FENG Xiufang

College of Mathematics and Computer, Ningxia University, Yinchuan 750021, China

Online:2013-12-01 Published:2016-06-12

摘要/Abstract

摘要： 利用修正的有限体积方法求解带有间断系数的泊松方程，改进是对基于笛卡尔坐标系下的调和平均系数进行的。数值实验表明新格式二阶逐点收敛并且在界面处具有二阶精度，新方法较已有的求解不连续扩散系数的算术平均法和调和平均法，特别是在系数跳跃较大的情况下更具优势。

关键词: 有限体积方法, 变系数椭圆方程, 界面问题

Abstract: In this paper, a new modified finite volume method is presented to solve the elliptic equations with discontinuous coefficients. This method allows discontinuities of the solution and normal derivatives on the interface inside the domain on a Cartesian grid. From experiment results, this scheme is second-order point-wise convergence and approximates the fluxes to second-order accuracy. At the same time, the numerical results show that the new scheme is much more accurate than the known schemes which use arithmetic and harmonic averaging in solving interface problems, especially in the cases of large jumps of coefficient.

Key words: finite volume method, elliptic equations with variable coefficients, interface problem

续小磊，冯秀芳. 求解带有间断系数泊松方程的修正有限体积[J]. 计算机工程与应用, 2013, 49(23): 35-38.

XU Xiaolei, FENG Xiufang. New modified finite volume approximation of elliptic equations with discontinuous coefficients[J]. Computer Engineering and Applications, 2013, 49(23): 35-38.