对流扩散方程的迎风变换及相应有限差分方法

A TRANSFORMATION OF THE CONVECTIVE DIFFUSION EQUATION WITH CORRESPONDING FINITE DIFFERENCE METHOD

本文提出所谓迎风变换,将对流扩散方程分解为对流迎风函数和扩散方程,并构造相应的有限差分格式。对流迎风函数以简明的指数解析形式反映对流扩散现象的迎风效应,原则上消除了源于不对称对流算子的困难,能够便利对流扩散方程的数值求解。有限差分格式具有二阶精度和无条件稳定性,算例表明其准确性、收敛速度及对边界层效应的适应能力均明显优于中心差分格式和迎风差分格式。

An analytical transformation with corresponding finite difference method of the convective diffusion equation into a diffusion equation coupled with a so-called upwind convection function is proposed in this paper. Reflecting the upwind effect in convective diffusion phenomena with a brief exponential representation, the upwind convection function reduces in essence the difficulty due to the non-symmetrical convection operator, and thus can bring great convenience to the numerical aspect of the convective diffusion equation. The proposed finite difference scheme is second-order consistent and unconditionally stable, and shows a high accuracy in illustrative computations.An analytical transformation with corresponding finite difference method of the convective diffusion equation into a diffusion equation coupled with a so-called upwind convection function is proposed in this paper. Reflecting the upwind effect in convective diffusion phenomena with a brief exponential representation, the upwind convection function reduces in essence the difficulty due to the non-symmetrical convection operator, and thus can bring great convenience to the numerical aspect of the convective diffusion equation. The proposed finite difference scheme is second-order consistent and unconditionally stable, and shows a high accuracy in illustrative computations.