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
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
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.
Fund: 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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