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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.6 P.1061~1067

10.1631/jzus.2006.A1061


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


Author(s):  LIU Xin

Affiliation(s):  Department of Mechanics, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   sdcxliu@zju.edu.cn

Key Words:  Radial basis functions, Radial point collocation method (RPCM), Collocation, Meshfree, Convection-diffusion


LIU Xin. Radial point collocation method (RPCM) for solving convection-diffusion problems[J]. Journal of Zhejiang University Science A, 2006, 7(6): 1061~1067.

@article{title="Radial point collocation method (RPCM) for solving convection-diffusion problems",
author="LIU Xin",
journal="Journal of Zhejiang University Science A",
volume="7",
number="6",
pages="1061~1067",
year="2006",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2006.A1061"
}

%0 Journal Article
%T Radial point collocation method (RPCM) for solving convection-diffusion problems
%A LIU Xin
%J Journal of Zhejiang University SCIENCE A
%V 7
%N 6
%P 1061~1067
%@ 1673-565X
%D 2006
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A1061

TY - JOUR
T1 - Radial point collocation method (RPCM) for solving convection-diffusion problems
A1 - LIU Xin
J0 - Journal of Zhejiang University Science A
VL - 7
IS - 6
SP - 1061
EP - 1067
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A1061


Abstract: 
In this paper, collocation method (RPCM)%29&ck%5B%5D=abstract&ck%5B%5D=keyword'>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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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

[4] Lee, C.K., Liu, X., Fan, S.C., 2003. Local multiquadric approximation for solving boundary value problems. Computational Mechanics, 30:396-409.

[5] Liu, G.R., 2002. Mesh Free Methods, Moving beyond the Finite Element Method. CRC Press.

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[7] Liu, G.R., Gu, Y.T., 2002. 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. Singapore, p.259-261.

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

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

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

[11] Onate, E., Idelsohn, S., Zienkiewicz, O.C., Taylor, R.L., 1996. A finite point method in computational mechanics. Applications to convective transport and fluid flow. Int. J. Numer. Methods Engrg., 39(22):3839-3866.

[12] Wu, Y.L., Liu, G.R., 2003. A meshfree formulation of local radial point interpolation method (LRPIM) for incompressible flow simulation. Computational Mechanics, 30(5-6):355-365.

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