A new complex variable meshless method for advection–diffusion problems

doi:10.1088/1674-1056/22/3/030208

Abstract In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, an improved complex variable meshless method (ICVMM) for two-dimensional advection–diffusion problems is developed. The equivalent functional of two-dimensional advection–diffusion problems is formed, the variation method is used to obtain the equation system, and the penalty method is employed to impose the essential boundary conditions. The difference method for two-point boundary value problems is used to obtain the discrete equations. Then the corresponding formulas of the ICVMM for advection–diffusion problems are presented. Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper. It is shown that the ICVMM is very effective for advection–diffusion problems, and has good convergent character, accuracy, and computational efficiency.

Keywords: meshless method improved complex variable moving least-square approximation improved complex variable meshless method advection–diffusion problem

Received: 13 August 2012
Revised: 27 August 2012
Accepted manuscript online:

PACS:	02.60.Cb	(Numerical simulation; solution of equations)
	02.60.Lj	(Ordinary and partial differential equations; boundary value problems)
	66.10.C-	(Diffusion and thermal diffusion)
	82.56.Lz	(Diffusion)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11171208), the Shanghai Leading Academic Discipline Project, China (Grant No. S30106), and the Innovation Fund for Graduate Student of Shanghai University, China (Grant No. SHUCX120125).

Corresponding Authors: Cheng Yu-Min
E-mail: ymcheng@shu.edu.cn

Cite this article:

Wang Jian-Fei (王健菲), Cheng Yu-Min (程玉民) A new complex variable meshless method for advection–diffusion problems 2013 Chin. Phys. B 22 030208

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