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
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
[1]   BOUNDARY-ELEMENT SOLUTION FOR STEADY AND UNSTEADY STOKES-FLOW [J].
ABOUSLEIMAN, Y ;
CHENG, AHD .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1994, 117 (1-2) :1-13
[2]   Finite cloud method: a true meshless technique based on a fixed reproducing kernel approximation [J].
Aluru, NR ;
Li, G .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2001, 50 (10) :2373-2410
[3]  
[Anonymous], 1974, RAIRO ANAL NUMER
[4]  
Armando Duarte C., 1996, Numerical methods for partial differential equations, V12, P673, DOI 10.1002/(SICI)1098-2426(199611)12:6
[5]  
Babuska I., 2003, Acta Numerica, V12, P1, DOI 10.1017/S0962492902000090
[6]   On the approximability and the selection of particle shape functions [J].
Babuska, I ;
Banerjee, U ;
Osborn, JE .
NUMERISCHE MATHEMATIK, 2004, 96 (04) :601-640
[7]   SPECIAL FINITE-ELEMENT METHODS FOR A CLASS OF 2ND-ORDER ELLIPTIC PROBLEMS WITH ROUGH COEFFICIENTS [J].
BABUSKA, I ;
CALOZ, G ;
OSBORN, JE .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1994, 31 (04) :945-981
[8]  
Babuska I, 1997, INT J NUMER METH ENG, V40, P727, DOI 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO
[9]  
2-N
[10]  
BABUSKA I, 2004, INT J COMPUT METHODS, V1, P1