中国物理B ›› 2013, Vol. 22 ›› Issue (3): 30208-030208.doi: 10.1088/1674-1056/22/3/030208

• GENERAL • 上一篇    下一篇

A new complex variable meshless method for advection–diffusion problems

王健菲, 程玉民   

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
  • 收稿日期:2012-08-13 修回日期:2012-08-27 出版日期:2013-02-01 发布日期:2013-02-01
  • 基金资助:
    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).

A new complex variable meshless method for advection–diffusion problems

Wang Jian-Fei (王健菲), Cheng Yu-Min (程玉民)   

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
  • Received:2012-08-13 Revised:2012-08-27 Online:2013-02-01 Published:2013-02-01
  • Contact: Cheng Yu-Min E-mail:ymcheng@shu.edu.cn
  • Supported by:
    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).

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摘要： 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.

关键词: meshless method, improved complex variable moving least-square approximation, improved complex variable meshless method, advection-diffusion problem

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.

Key words: meshless method, improved complex variable moving least-square approximation, improved complex variable meshless method, advection–diffusion problem

中图分类号:  (Numerical simulation; solution of equations)

  • 02.60.Cb
02.60.Lj (Ordinary and partial differential equations; boundary value problems) 66.10.C- (Diffusion and thermal diffusion) 82.56.Lz (Diffusion)