中国物理B ›› 2013, Vol. 22 ›› Issue (8): 80203-080203.doi: 10.1088/1674-1056/22/8/080203

• GENERAL • 上一篇    下一篇

A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems

王启防a, 戴保东a, 栗振锋b   

  1. a Department of Engineering Mechanics, Taiyuan University of Science & Technology, Taiyuan 030024, China;
    b College of Transportation & Logistics, Taiyuan University of Science & Technology, Taiyuan 030024, China
  • 收稿日期:2013-01-28 修回日期:2013-03-28 出版日期:2013-06-27 发布日期:2013-06-27
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 51078250), the Research Project by Shanxi Scholarship Council of Shanxi Province, China (Grant No. 2013-096), and the Scientific & Technological Innovation Program for Postgraduates of Taiyuan University of Science and Technology, China (Grant No. 20125026).

A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems

Wang Qi-Fang (王启防)a, Dai Bao-Dong (戴保东)a, Li Zhen-Feng (栗振锋)b   

  1. a Department of Engineering Mechanics, Taiyuan University of Science & Technology, Taiyuan 030024, China;
    b College of Transportation & Logistics, Taiyuan University of Science & Technology, Taiyuan 030024, China
  • Received:2013-01-28 Revised:2013-03-28 Online:2013-06-27 Published:2013-06-27
  • Contact: Dai Bao-Dong E-mail:Dai_baodong@126.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 51078250), the Research Project by Shanxi Scholarship Council of Shanxi Province, China (Grant No. 2013-096), and the Scientific & Technological Innovation Program for Postgraduates of Taiyuan University of Science and Technology, China (Grant No. 20125026).

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摘要： On the basis of the complex variable moving least-square (CVMLS) approximation, a complex variable meshless local Petrov-Galerkin (CVMLPG) method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional (2D) problem is formed with a one-dimensional (1D) basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method (FEM). This comparison illustrates the accuracy as well as the capability of the CVMLPG method.

关键词: meshless method, complex variable moving least-square method, complex variable meshless local Petrov-Galerkin method, transient heat conduction problems

Abstract: On the basis of the complex variable moving least-square (CVMLS) approximation, a complex variable meshless local Petrov-Galerkin (CVMLPG) method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional (2D) problem is formed with a one-dimensional (1D) basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method (FEM). This comparison illustrates the accuracy as well as the capability of the CVMLPG method.

Key words: meshless method, complex variable moving least-square method, complex variable meshless local Petrov-Galerkin method, transient heat conduction problems

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)