CLC number: O302; O451
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 0000-00-00
Cited: 4
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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.
[1] Donea, J., Roig, B., Huerta, A., 2000. High-order accurate time-stepping schemes for convection-diffusion problems. Comput. Methods Appl. Mech. Engrg., 182:249-275.
[2] Kansa, E.J., 1990. Multiquadrics, a scattered data approximation scheme with applications to computational fluid-dynamics. Comput. Math. and Appl., 19:147-161.
[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.
[6] Liu, G.R., Gu, Y.T., 2001. Point interpolation method for two-dimension solids. Int. J. Numer. Methods Eng., 50(4):937-951.
[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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