计算力学学报2016，Vol.33Issue(6)：874-880,7.DOI:10.7511/jslx201606012
一种基于 Associated Hermite 正交函数求解对流扩散方程的算法
A new method for solving convection-diffusion equation using Associated Hermite orthogonal functions
摘要
Abstract
In this work ,an unconditionally stable method using the Associated Hermite (AH) orthogonal functions for solving the convection‐diffusion equation is proposed .T he time derivatives in the equation are expanded by the weighted Hermite functions .By introducing the Galerkin temporal testing procedure to the expanded equation ,the time variable can be eliminated in the process of calculation .An implicit difference equation can then be obtained in A H domain under no convergent conditions .T he numerical results of the equation can be obtained by solving the expanded coefficients in A H domain recursively . Two numerical examples were conducted to validate the accuracy and the efficiency of the proposed method by comparing to the conventional finite difference method and the alternating direction implicit (ADI) method .The numerical results have shown that the accuracy of this unconditionally stable method is independent of the time step size ,and this proposed method has great advantage in efficiency in a computational domain with fine structure in convection‐diffusion problems .Moreover ,the agreement between the results obtained using the FD method and the proposed method is very good .关键词
Hermite多项式/无条件稳定算法/有限差分法/对流扩散方程/ADIKey words
Hermite polynomials/unconditionally/finite difference/convection-diffusion equation/ADI分类
数理科学引用本文复制引用
张迪,缪小平,彭福胜,江丰,魏子杰..一种基于 Associated Hermite 正交函数求解对流扩散方程的算法[J].计算力学学报,2016,33(6):874-880,7.基金项目
江苏省自然科学基金（BK20131067）资助项目． （）
