积分节点迎风偏移的节点积分无单元Galerkin方法  

Nodal Integration Element-free Galerkin Method with Upwind Shifted Integration Nodes

作　　者：王晓东[1] 欧阳洁[1] 王玉龙[1] 蒋涛[1] 

机构地区：[1]西北工业大学应用数学系,西安710129

出　　处：《计算物理》2012年第2期183-190,共8页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(10871159);教育部博士研究生学术新人奖;西北工业大学博士论文创新基金(cx201019)资助项目

摘　　要：建立求解稳态对流-扩散方程的一种稳定、高效的无单元Galerkin方法.该方法计算积分时采用基于局部Taylor展开的节点积分,并根据对流占优的程度对积分节点进行自适应迎风偏移.与传统的使用稳定化的无单元Galerkin方法相比,该方法是一种不依赖于背景网格积分的纯无网格方法,具有更好的稳定性和较高的计算效率,其程序实施更为简便.A stable and efficient element-free Galerkin method is proposed for steady convection-diffusion problems.In the method integrations are computed with a local Taylor expansion nodal integral technique.According to convection-dominated degree,integration nodes are adaptively shifted opposite to the streamline direction.Compared with conventional element-free Galerkin method with stabilization,the method exhibits better stability and higher efficiency in solving convection-dominated convection-diffusion problems.It is a pure meshfree method,which is independent of background integral.Moreover,the method is easy to be implemented.

关 键 词：无单元Galerkin方法 无网格方法 节点积分 对流-扩散 迎风偏移 

分 类 号：O241[理学—计算数学]