Chin. Phys. B ›› 2012, Vol. 21 ›› Issue (12): 120206-120206.doi: 10.1088/1674-1056/21/12/120206

• GENERAL • 上一篇    下一篇

A new complex variable meshless method for transient heat conduction problems

王健菲a b, 程玉民a b   

  1. a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
    b Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
  • 收稿日期:2012-05-16 修回日期:2012-06-03 出版日期:2012-11-01 发布日期:2012-11-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11171208), and the Shanghai Leading Academic Discipline Project, China (Grant No. S30106), and the Innovation Fund for Graduate Student of Shanghai University of China (Grant No. SHUCX120125).

A new complex variable meshless method for transient heat conduction problems

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

  1. a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
    b Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China
  • Received:2012-05-16 Revised:2012-06-03 Online:2012-11-01 Published:2012-11-01
  • 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), and the Shanghai Leading Academic Discipline Project, China (Grant No. S30106), and the Innovation Fund for Graduate Student of Shanghai University of China (Grant No. SHUCX120125).

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摘要： In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, a new complex variable meshless method (CVMM) for two-dimensional (2D) transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper.

关键词: meshless method, improved complex variable moving least-square approximation, complex variable meshless method, transient heat conduction problem

Abstract: In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, a new complex variable meshless method (CVMM) for two-dimensional (2D) transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper.

Key words: meshless method, improved complex variable moving least-square approximation, complex variable meshless method, transient heat conduction 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) 44.10.+i (Heat conduction)