Radial point collocation method (RPCM) for solving convection-diffusion problems

被引：0

作者：

Liu X. ^{[1
]}

机构：

[1] Department of Mechanics, Zhejiang University

来源：

Journal of Zhejiang University-SCIENCE A | 2006年 / 7卷 / 6期

基金：

中国国家自然科学基金;

关键词：

Collocation; Convection-diffusion; Meshfree; Radial basis functions; Radial point collocation method (RPCM);

D O I：

10.1631/jzus.2006.A1061

中图分类号：

学科分类号：

摘要：

In this paper, Radial point collocation method (RPCM), a kind of meshfree method, is applied to solve convection-diffusion problem. The main feature of this approach is to use the interpolation schemes in local supported domains based on radial basis functions. As a result, this method is local and hence the system matrix is banded which is very attractive for practical engineering problems. In the numerical examination, RPCM is applied to solve non-linear convection-diffusion 2D Burgers equations. The results obtained by RPCM demonstrate the accuracy and efficiency of the proposed method for solving transient fluid dynamic problems. A fictitious point scheme is adopted to improve the solution accuracy while Neumann boundary conditions exist. The meshfree feature of the present method is very attractive in solving computational fluid problems.

引用

页码：1061 / 1067

页数：6

共 12 条

[1]

Donea J., Roig B., Huerta A., High-order accurate time-stepping schemes for convection-diffusion problems, Comput. Methods Appl. Mech. Engrg., 182, pp. 249-275, (2000)

[2]

Kansa E.J., Multiquadrics, a scattered data approximation scheme with applications to computational fluid-dynamics, Comput. Math. and Appl., 19, pp. 147-161, (1990)

[3]

Kansa E.J., Hon Y.C., Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations, Computers and Math. Appl., 39, pp. 123-137, (2000)

[4]

Lee C.K., Liu X., Fan S.C., Local multiquadric approximation for solving boundary value problems, Computational Mechanics, 30, pp. 396-409, (2003)

[5]

Liu G.R., Mesh Free Methods, Moving beyond the Finite Element Method, (2002)

[6]

Liu G.R., Gu Y.T., Point interpolation method for two-dimension solids, Int. J. Numer. Methods Eng., 50, 4, pp. 937-951, (2001)

[7]

Liu G.R., Gu Y.T., A truly meshless method based on the strong-weak form. Advances in meshfree and X-FEM methods, Proceeding of the 1st Asian Workshop in Meshfree Methods, pp. 259-261, (2002)

[8]

Liu G.R., Gu Y.T., A meshfree method: Meshfree weak-strong (MWS) form method, for 2-D solids, Computational Mechanics, 33, 1, pp. 2-14, (2003)

[9]

Liu X., Liu G.R., Tai K., Lam K.Y., Radial point interpolation collocation method (RPICM) for the solution of nonlinear Poisson problems, Computational Mechanics, 36, 4, pp. 298-306, (2005)

[10]

Liu X., Liu G.R., Tai K., Lam K.Y., Radial point interpolation collocation method for the solution of partial differential equations, Computers and Mathematics with Applications, 50, pp. 1425-1442, (2005)

← 1 2 →