%0 Journal Article
%T A universal numerical discretization method on different meshes<br>各种网格上统一的数值离散方法
%A Cai Qingdong State Key Laboratory of Turbulence
%A Complex System
%A Peking University
%A Beijing
%A China
%A <br>蔡庆东
%J 力学学报
%D 2004
%I 
%X A universal discretization method is prestented in this paper, it can be used on arbitary meshes. Considering the common properties of all different kinds of meshes, we established this numerical difference scheme by Taylor series expansion and the least square method. We can obtain the local difference matrix(LDM) and global difference matrix(GDM) on any mesh by this method, then the difference operator can be interpreted as its matrix form in discreted space directly. This skill can apply to many numerical schemes developed on structured grid, then those schemes will work on arbitary meshes, the complexity of the computation domain will no longer be any problems. In order to verify the skill in this paper, we first compute the numerical difference of an analytical function, and compare the results with the exact solutions. It shows that the method has the 2nd order accuracy as the center difference scheme. Another two examples are numerical simulation of incompressible flow in a two dimension backward-facing step and three dimension driven cavity. The vorticity-stream function equation and Navier-Stokes equations in velocity-pressure form are used respectively. The results in this paper are agreement with the classical ones on structured meshes. But the method here can be applied on any grid.
%K numerical method
%K mesh
%K difference matrix
%K incompressible flow<br>数值方法
%K 计算网格
%K 微分矩阵
%K 不可压缩流
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=5D344E2AD54D14F8&jid=4100DA4A1A3BA1B0CE5AD99AE1DFB420&aid=06869A891BB8E78E&yid=D0E58B75BFD8E51C&vid=933658645952ED9F&iid=E158A972A605785F&sid=23F20F9780C3579E&eid=8ACD9060100C26F1&journal_id=0459-1879&journal_name=力学学报&referenced_num=0&reference_num=15