改进节点积分的无单元Galerkin法及其在流动问题中的应用  

An improved nodal integration Element-Free Galerkin method and its application in flow problems

作　　者：王玉龙[1] 欧阳洁[1] 王晓东[1] 蒋涛[1] 

机构地区：[1]西北工业大学理学院应用数学系,陕西西安710129

出　　处：《空气动力学学报》2012年第3期358-364,共7页Acta Aerodynamica Sinica

基　　金：国家自然科学基金(10871159)

摘　　要：无单元Galerkin法需要在背景网格上积分,计算量大,且在求解对流占优问题时会出现非物理的数值伪振荡现象。为此,基于局部Taylor展开思想,采用节点处的局部Taylor展开计算积分,建立了局部Taylor展开积分无单元Galerkin法。该方法同时解决了标准的无单元Galerkin法计算量大和对流占优时会出现数值伪振荡的问题。一维定常对流扩散方程和二维Burgers方程的求解说明了该方法的有效性,且计算效率远高于无单元Galerkin法。Element-Free Galerkin（EFG） method is intensive computation due to the requirement of back- ground cells quadrature, and may appear non-physical oscillations in solving convection dominated problems. To solve these problems, a local Taylor expansion integration Element-Free Galerkin （LTEI-EFG） method is proposed in this paper, which based on the idea of integration for local Taylor expansion. This method can not only save computation cost but also eliminate non-physical oscillation in solving convection dominated problem. Numerical examples of one-dimensional convection diffusion equation and two-dimensional Burgers＇ equation show that the I.TEI-EFG method is accurate and much more efficient than EFG method.

关 键 词：无网格法 局部Taylor展开 节点积分 对流占优 

分 类 号：O241[理学—计算数学] O242[理学—数学]