对流扩散方程的二阶紧凑迎风差分格式

The Compact Second-Order Upwind Finite Difference Schemes for the Convection-Diffusion Equations

本文通过差分格式的摄动处理,提出对流扩散方程的二阶紧凑迎风差分格式。该二阶格式只涉及相邻网格点,具有无条件稳定性,形式与经典一阶迎风格式相同,惟扩散系数中出现简单的对流修正。本文并作一、二、三维流动模型方程及高Rayleigh数自然对流传热问题的数值求解,例示该格式的良好性态。

The compact second- order upwind finite difference schemes free of cell Reynolds number limitation are developed in this paper for the one-to three-dimensional steady convection diffusion equations, using a perturbational technique applied to the classical first-order upwind schemes. The present second-order schemes take essentially the same form as those of the first order schemes, but involve a simple modification to the diffusive coefficients. Numerical examples including one-to three-dimensional model equations of fluid flow and a problem of natural convection with boundary-layer effect are given to illustrate the excellent behavior of the present schemes.