求解泊松方程的紧致修正法  

Compact correction method for Poisson equation

作　　者：张昆[1] 杨茉[1] 

机构地区：[1]上海理工大学动力工程学院,上海200093

出　　处：《水动力学研究与进展（A辑）》2011年第4期422-429,共8页Chinese Journal of Hydrodynamics

基　　金：国家自然科学基金资助项目(50876067);上海市教委发展基金项目(J50501)资助

摘　　要：将紧致格式与低阶格式结合,构造紧致格式的修正项,并将修正项加入到源项中进行求解,得到了一种基于非均分网格求解泊松方程的紧致修正法,且将该方法应用于二维和三维泊松方程的数值求解中。数值计算结果表明:紧致修正方法的精度高于经典方法的精度,但四阶紧致修正方法比二阶经典方法对网格的依赖性强。In this paper combining the compact finite difference scheme with the classical finite difference scheme,the compact correction term was established and it was added to the source term.Then a new compact correction method for solving Poisson equation was developed on non-uniform grids.This method was applied to solving 2D or 3D Poisson equation.The results show that compact method has higher accuracy than the classical method,and the 4-order compact scheme is more sensitive to grid ratio than the 2-order classical scheme.

关 键 词：泊松方程 非等距网格 紧致差分格式 紧致修正法 

分 类 号：O241.3[理学—计算数学]