中国物理B ›› 2013, Vol. 22 ›› Issue (3): 30208-030208.doi: 10.1088/1674-1056/22/3/030208
王健菲, 程玉民
Wang Jian-Fei (王健菲), Cheng Yu-Min (程玉民)
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.
中图分类号: (Numerical simulation; solution of equations)