对流占优问题的无网格稳定化方法  

Stabilization Meshless Method for Convection Dominated Problems

作　　者：张小华[1] 欧阳洁[1] 王建瑜[1] 鲁传敬 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《应用数学和力学》2008年第8期967-975,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(重大)资助项目(10590353);陕西省自然科学基金资助项目(2005A16)

摘　　要：应用标准的无网格方法求解对流占优问题时会出现数值伪振荡.针对此问题,给出了无网格方法中消除非稳定数值解的4种技术,即节点加密、增大节点影响半径、完全迎风无网格稳定化方法、自适应无网格稳定化方法.并将这4种技术应用于径向点插值方法求解一维或二维对流扩散方程.数值结果表明这4种技术均能有效地消除对流占优时的数值伪振荡现象,且自适应迎风无网格稳定化方法是4种技术中最有效的.It is well known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. Several techniques were proposed to overcome the instability issues in convection-dominated problems simulated by meshless method. These stable techniques included, the nodal refinement, the enlargement of nodal influence domain, the full upwind meshless technique and the adaptive upwind meshless technique. Meanwile, these stable techniques were applied to RPIM to solve one and two-dimensional convection-diffusion equations. Numerical results for example problems show that these techniques are effective to solve convection-dominated problems, and the adaptive upwind meshless technique is the most effective method of all.

关 键 词：无网格方法 对流扩散方程 稳定化方法 

分 类 号：O35[理学—流体力学] O241[理学—力学]