对流占优问题的无网格稳定化方法

张小华; 欧阳洁; 王建瑜

对流占优问题的无网格稳定化方法

西北工业大学应用数学系,西安 710072

基金项目: 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)

详细信息

作者简介:
张小华(1980- ),男,湖北枝江人,博士生(E-mail:chafen03@mail.nwpu.edu.cn);欧阳洁(1957- ),女,教授,博士(联系人.Tel:十8Cr29-88495234).

中图分类号: O35;O241
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出版历程
- 收稿日期: 2007-09-20
- 修回日期: 2008-06-26
- 刊出日期: 2008-08-15

Stabilization Meshless Method for Convection Dominated Problems

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P. R. China

摘要

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．
- 无网格方法 /
- 对流扩散方程 /
- 稳定化方法
Abstract: It is well luiown that the standard Galerlan 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 enlazgement 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 resalts for example problems show that these techniques are effective to solve convection-dominated preblems,and the adaptive upwind meshless technique is the most effective method of all.
- meshless method /
- convection-digusion problems /
- stability methods

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参考文献(12)

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对流占优问题的无网格稳定化方法

作者简介:
张小华(1980- ),男,湖北枝江人,博士生(E-mail:chafen03@mail.nwpu.edu.cn);欧阳洁(1957- ),女,教授,博士(联系人.Tel:十8Cr29-88495234).

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Stabilization Meshless Method for Convection Dominated Problems

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对流占优问题的无网格稳定化方法

作者简介: 张小华(1980- ),男,湖北枝江人,博士生(E-mail:chafen03@mail.nwpu.edu.cn);欧阳洁(1957- ),女,教授,博士(联系人.Tel:十8Cr29-88495234).

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出版历程

Stabilization Meshless Method for Convection Dominated Problems

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出版历程

目录

作者简介:
张小华(1980- ),男,湖北枝江人,博士生(E-mail:chafen03@mail.nwpu.edu.cn);欧阳洁(1957- ),女,教授,博士(联系人.Tel:十8Cr29-88495234).