基于MQ-RBF-FD求解对流扩散方程的二阶算法

doi:10.3976/j.issn.1002-4026.2020.05.014

Shandong Science ›› 2020, Vol. 33 ›› Issue (5): 113-118.doi: 10.3976/j.issn.1002-4026.2020.05.014

• Other Research Article • Previous Articles Next Articles

A novel second-order algorithm based on MQ-RBF-FD method for solving convection diffusion equation

YAO Lin，TANG Quan *

School of Mathematical Sciences，Xinjiang Normal University, Urumqi 830017，China

Received:2020-02-07 Online:2020-10-08 Published:2020-09-27

Abstract

Abstract: To solve the unsteady convection diffusion equation, we propose a new second-order algorithm that applies the multi-quadrics localized radial basis function(MQ-RBF-FD)method and dimension-splitting method for spatial discretization, and BDF2 methods and alternating iterative schemes for temporal discretization. We determine the appropriate number of iterations, choose an optimal shape parameter c, and finally, obtain higher order accuracy. We conducted numerical experiments to verify the rationality and feasibility of the theoretical results.

Key words: convection diffusion, RBF-FD method, shape parameter, higher order accuracy, iterative schemes

CLC Number:

O241.82

YAO Lin, TANG Quan. A novel second-order algorithm based on MQ-RBF-FD method for solving convection diffusion equation[J].Shandong Science, 2020, 33(5): 113-118.

References 12

1	胡健伟, 汤怀民. 偏微分方程数值方法[M]. 北京: 科学出版社, 1999.
2	陆金甫, 关治. 偏微分方程数值解法[M]. 北京: 清华大学出版社, 2016.
3	FORNBERG B. Generation of finite difference formulas on arbitrarily spaced grids[J].Mathematics of Communication, 1988, 51(184):699-706. doi: 10.2307/2008770
4	DENG S H, WANG G Z. Numerical analysis of the progressive iterative approximation method[J]. Journal of Computer Aided Design & Computer Graphics, 2012, 24(7): 879-884. doi: 10.3969/j.issn.1003-9775.2012.07.006
5	BAYONA V, MOSCOSO M, CARRETERO M, et al. RBF-FD formulas and convergence properties[J]. Journal of Computational Physics, 2010, 229(22): 8281-8295. doi: 10.1016/j.jcp.2010.07.008
6	章本照, 印建安, 张宏基. 流体力学数值方法[M]. 北京: 机械工业出版社, 2003.
7	LI N, SU H Y, GUI D W, et al. Multi-quadric RBF-FD method for the convectiondominated diffusion problems base on Shishkin nodes[J]. International Journal of Heat and Mass Transfer, 2018, 118: 734-745. doi: 10.1016/j.ijheatmasstransfer.2017.11.011
8	GEISER J. Iterative operator-splitting methods with higher-order time integration methods and applications for parabolic partial differential equations[J]. Journal of Computational and Applied Mathematics, 2008, 217(1): 227-242. doi: 10.1016/j.cam.2007.06.028
9	ANGELINI O, BRENNER K, HILHORST D. A finite volume method on general meshes for a degenerate parabolic convectionreactiondiffusion equation[J]. Numerische Mathematik, 2013, 123(2): 219-257. doi: 10.1007/s00211-012-0485-5
10	ZHANG Y G, MA T F, WANG Y, et al. High order compact difference scheme for solving the unsteady convection diffusion reaction equation[J]. Mathematics in Practice and Theory, 2017, 47(13): 263-270.
11	李荣华, 刘播. 微分方程数值解法[M].4版. 北京: 高等教育出版社, 2009.
12	GEISER J, TANOGˇLU G, GCYENEN N. Higher order operator splitting methods via Zassenhaus product for Mula: theory and applications[J]. Computers & Mathematics With Applications, 2011, 62(4): 19942015. doi: 10.1016/j.camwa.2011.06.043

[1]	GUO Fei-fan, ZHANG Xin-dong, WANG Shuo. Numerical solution for convection-diffusion equation with time fractional variable coefficients [J]. Shandong Science, 2020, 33(1): 116-123.
[2]	CHEN Fan. Semi-discrete discontinuous finite volume element method for unsaturated soil water flow problem [J]. SHANDONG SCIENCE, 2018, 31(5): 95-100.

A novel second-order algorithm based on MQ-RBF-FD method for solving convection diffusion equation

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References 12

Related Articles 2

Metrics

Comments

Recommended 0