求解带有间断系数二维扩散方程的修正有限体积方法

A Modified Finite Volume Approximation of 2-Dimensional Diffusion Equation With Discontinuous Coefficients

针对具有间断系数的二维扩散方程,通过改进通量函数和调和平均系数的求解方法,提出了一种修正的有限体积方法.新方法得到的是无条件稳定的隐格式.数值实验结果表明该方法在处理间断系数问题时较经典的有限体积方法更为有效.

A new modified finite volume method was presented to solve the 2-dimensional dif- fusion equation. Through improvement of the methods for solving the flux function and harmon- ic average coefficient, a new ~difference scheme was obtained for the diffusion equation with discontinuous coefficients. This scheme was an implicit difference scheme and was uncondition- ally stable. Subsequent numerical tests show that the presented method is more accurate than the classical finite volume method.