对流占优扩散问题的一种特征差分方法

用基于一般的 L agrange插值的特征差分方法求解对流占优扩散问题 ,会出现较大的数值扩散或者数值振荡等困难 ,高阶单调插值又计算复杂。该文采用 A.A .Sam arskii构造差分格式的方法 ,建立了一种新的特征差分方法。先对对流扩散方程的扩散项进行修改 ,然后再进行特征差分。此方法具有较高精度 ,并消除了非物理振荡。证明了方法的无条件稳定性。数值结果表明 ,该方法可成功求解对流占优扩散问题。

Characteristic difference method for the convection-dominated diffusion problems

When characteristic difference methods basis on normal Lagrange interpolation are used to solve convection-dominated diffusion problems, numerical difficulties occur such as numerical oscillations or numerical diffusion. The higher-order monotone interpolation method would be more effective but it is too complicated. In this paper, a new characteristic difference scheme based on the characteristic difference technique is presented for the convection diffusion eqution. The Samarskii's perturbation method is used to deal with the diffusion term. This method is precise, non-oscillatory and unconditionally stable. Numerical simulations also show that the method can accurately solve convection- dominated diffusion problems.