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 引用本文: 张小华, 欧阳洁, 王建瑜. 对流占优问题的无网格稳定化方法[J]. 应用数学和力学, 2008, 29(8): 967-975.
ZHANG Xiao-hua, OUYANG Jie, WANG Jian-yu. Stabilization Meshless Method for Convection Dominated Problems[J]. Applied Mathematics and Mechanics, 2008, 29(8): 967-975.
 Citation: ZHANG Xiao-hua, OUYANG Jie, WANG Jian-yu. Stabilization Meshless Method for Convection Dominated Problems[J]. Applied Mathematics and Mechanics, 2008, 29(8): 967-975.

## 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).
• 中图分类号: O35;O241

## Stabilization Meshless Method for Convection Dominated Problems

• 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．
•  [1] Donea J,Huerta A.Finite Element Methods for Flow Problems[M].Chichester:Wiley,2003. [2] Monaghan J J.An introduction to SPH[J].Computer Physics Communications,1988,48(1):89-96. [3] Liu W K, Jun S, Zhang Y F.Reproducing kernel particle methods[J].International Journal for Numerical Methods in Fluids,1995,20(8/9):1081-1106. [4] Liu W K, Jun S, Sihling D T,et al.Multiresolution reproducing kernel particle method for computational fluid dynamics[J].International Journal for Numerical Methods in Fluids,1997,24(12):1391-1415. [5] Liu G R, Gu Y T.An Introduction to Meshfree Methods and Their Programming[M].Dordrecht: Springer,2005. [6] Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods[J].International Journal for Numerical Methods in Engineering,1994,37(2):229-256. [7] Oate E, Idelsohn S, Zienkiewicz O C.A finite point method in computational mechanics: Application to convections to transport and fluid flow[J].International Journal for Numerical Methods in Engineering,1996,39(22):3839-3866. [8] Oate E,Idelsohn S, Zienkiewicz O C,et al.A stabilized finite point method for analysis of fluid mechanics problems[J].Computer Methods in Applied Mechanics and Engineering,1996,139(1/4):315-346. [9] Oate E,Idelsohn S.A mesh-free finite point method for advective-diffusive transport and fluid flow problems[J].Computational Mechanics,1998,21(4/5):283-292. [10] Lin H, Atluri S N. The meshless local Petrov-Galerkin (MLPG) method for convection-dynamics[J].Computer Modeling in Engineering and Sciences,2000,1(2):45-60. [11] 张小华,欧阳洁.线性定常对流占优对流扩散问题的无网格解法[J].力学季刊,2006,27(2):220-226. [12] 张雄, 刘岩. 无网格法[M].北京:清华大学出版社,2004.

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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

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