摘要
本文给出了一种求解非线性对流扩散方程:Burgers方程的算子分裂法,用显式差分格式处理扩散算子,用特征线法处理纯对流算子。并分析了算法的稳定性条件。然后,对一、二维Burgers方程进行数值解,所得结果与分析解或已有数值解吻合,表明了算法的有效性。
An operator-splitting algorithm for nonlinear advective diffusion equations——Burger's equations is presented. Explicit difference scheme and the method of characteristics are adopted for treating diffusion and advective operators respectively. Conditions for stability of the algorithm are also analyzed. Satisfactory agreements between numerical results of two examples using the present numerical procedure and the corresponding analytical or numerical solutions obtained by previous investigators are achieved, which manifests the potential efficacy of the splitting algorithm applied to simulations of viscous fluid flow and other advective diffusion process.
关键词
对流
扩散
算子分裂法
稳定性
advection
diffusion
stability
fractional step method
