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Chin. Phys. B, 2013, Vol. 22(9): 090204    DOI: 10.1088/1674-1056/22/9/090204
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Analysis of variable coefficient advection–diffusion problems via complex variable reproducing kernel particle method

Weng Yun-Jiea b, Cheng Yu-Mina
a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;
b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China
Abstract  The complex variable reproducing kernel particle method (CVRKPM) of solving two-dimensional variable coefficient advection-diffusion problems is presented in this paper. The advantage of the CVRKPM is that the shape function of a two-dimensional problem is formed with a one-dimensional basis function. The Galerkin weak form is employed to obtain the discretized system equation, and the penalty method is used to apply the essential boundary conditions. Then the corresponding formulae of the CVRKPM for two-dimensional variable coefficient advection-diffusion problems are obtained. Two numerical examples are given to show that the method in this paper has greater accuracy and computational efficiency than the conventional meshless method such as reproducing the kernel particle method (RKPM) and the element-free Galerkin (EFG) method.
Keywords:  meshless method      reproducing kernel particle method (RKPM)      complex variable reproducing kernel particle method (CVRKPM)      advection-diffusion problem  
Received:  16 December 2012      Revised:  26 February 2013      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) and the Leading Academic Discipline Project of Shanghai City, China (Grant No. S30106).
Corresponding Authors:  Cheng Yu-Min     E-mail:  ymcheng@shu.edu.cn

Cite this article: 

Weng Yun-Jie, Cheng Yu-Min Analysis of variable coefficient advection–diffusion problems via complex variable reproducing kernel particle method 2013 Chin. Phys. B 22 090204

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