| .流动问题无网格Galerkin方法的稳定化方案研究[J].计算力学学报,2008,25(6): |
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| 流动问题无网格Galerkin方法的稳定化方案研究 |
| Stabilization techniques based Element Free Galerkin method for flow problems |
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| DOI：10.7511/jslx20086159 |
| 中文关键词: 无网格,对流占优,纯对流,稳定化 |
| 英文关键词:EFG(Element Free Galerkin),convection dominated,pure convection,stabilization |
| 基金项目: |
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| 西北工业大学应用数学系 |
| 摘要点击次数: 2590 |
| 全文下载次数: 279 |
| 中文摘要: |
| 直接运用无网格Galerkin方法求解对流占优的非线性对流扩散方程及纯对流方程,会出现数值伪振荡现象。本文基于无网格Galerkin方法,构造了MFSUPG(Meshfree Streamline Upwind Petrov-Galerkin),MF-GLS(Meshfree Galerkin Least-Square),MFSGS(Meshfree Sub-Grid Scale)及MFLS(Meshfree Least-Square)四种稳定化方案。数值实验表明:四种稳定化方案中,MFLS的通用性最强。耦合MFLS的无网格Galerkin方法能很好地求解对流占优的非线性对流扩散方程及纯对流方程,具有计算精度高、稳定性好、前后处理方便、算法实施简单的优点,并能捕捉解的大梯度变化。 |
| 英文摘要: |
| The numerical solution may be corrupted by non-physical oscillations when Element Free Galerkin(EFG) method is directly used to solve convection dominated problems or pure convection equation.In order to eliminate spurious oscillations,the stabilization techniques,such as Meshfree Streamline Upwind Petrov-Galerkin,Galerkin Least Square,Sub-Grid Scale and Meshfree Least Square,were coupled with EFG method.They are written as the method of MFSUPG,MFGLS,MFSGS and MFLS.Several presented numerical examples show that these techniques can be used for solving the problems of convection dominated and pure convection since spurious oscillations can be largely restrained.Moreover,the MFLS method is the best one among above mentioned method because it can make error and spurious oscillation least in most cases.That is,it has high accuracy and good stabilization.Both pre-process and post-process are also convenient very much due to without mesh generation,so the corresponding algorithms can be easily implemented.Especially,the sharp change of solution can be nicely caught by using the MFLS method. |
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