Stabilization Meshless Method for Convection Dominated Problems
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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.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.
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Key words:
- meshless method /
- convection-digusion problems /
- stability methods
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