A meshless Galerkin method for Stokes problems using boundary integral equations

被引：57
作者：
Li, Xiaolin [1 ]
Zhu, Jialin [1 ]
机构：
[1] Chongqing Univ, Coll Math & Phys, Chongqing 400044, Peoples R China
来源：
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2009年 / 198卷 / 37-40期
关键词：
Stokes equations; Galerkin approximation; Boundary node method; Moving least-squares; Boundary integral equations; Meshless; FINITE-ELEMENT-METHOD; REPRODUCING KERNEL METHODS; CLOUD METHOD; SHAPE FUNCTIONS; NODE METHOD; APPROXIMATION; CONVERGENCE; EXTERIOR; STEADY; FLOWS;
D O I：
10.1016/j.cma.2009.04.009
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
A meshless Galerkin scheme for the simulation of two-dimensional incompressible viscous fluid flows in primitive variables is described in this paper. This method combines a boundary integral formulation for the Stokes equation with the moving least-squares (MLS) approximations for construction of trial and test functions for Galerkin approximations. Unlike the domain-type method, this scheme requires only a nodal structure on the bounding surface of a body for approximation of boundary unknowns, thus it is especially suitable for the exterior problems. Compared to other meshless methods such as the boundary node method and the element free Galerkin method, in which the MLS is also introduced, boundary conditions do not present any difficulty in using this meshless method. The convergence and error estimates of this approach are presented. Numerical examples are also given to show the efficiency of the method. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码：2874 / 2885
页数：12
相关论文
共 41 条
[21]  
Ladyzhenskaya O A., 1969, The Mathematical Theory of Viscous Incompressible Flow, V2nd ed.
[22]  
LANCASTER P, 1981, MATH COMPUT, V37, P141, DOI 10.1090/S0025-5718-1981-0616367-1
[23]   Boundary cloud method: a combined scattered point/boundary integral approach for boundary-only analysis [J].
Li, G ;
Aluru, NR .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2002, 191 (21-22) :2337-2370
[24]  
Li S., 2004, Meshfree particle methods
[25]   Moving least-square reproducing kernel method .2. Fourier analysis [J].
Li, SF ;
Liu, WK .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1996, 139 (1-4) :159-193
[26]   A Galerkin boundary node method and its convergence analysis [J].
Li, Xiaolin ;
Zhu, Jialin .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 230 (01) :314-328
[27]  
LIOUS JL, 1972, NONHOMOGENEOUS BOUND
[28]  
Liu G.-R., 2005, An Introduction to Meshfree Methods and Their Programming, DOI [DOI 10.1007/1-4020-3468-7, DOI 10.1017/CBO9781107415324.004]
[29]   Reproducing kernel element method. Part I: Theoretical formulation [J].
Liu, WK ;
Han, WM ;
Lu, HS ;
Li, SF ;
Cao, H .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2004, 193 (12-14) :933-951
[30]   Moving least-square reproducing kernel methods .1. Methodology and convergence [J].
Liu, WK ;
Li, SF ;
Belytschko, T .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1997, 143 (1-2) :113-154
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