对流扩散方程的二次单调插值特征差分方法

Quadratic monotone interpolation characteristic difference method for convection diffusion equation

特征差分方法适合于求解对流占优扩散问题 ,但也存在着精度低或非物理振荡等缺点。为克服其不足 ,建立和研究了二次单调插值特征差分方法。此方法具有较高精度并消除了非物理振荡。方法是无条件稳定的。用交替分组显式(AGE)方法求解了差分方程 ,方法便于并行计算。数值结果表明 。

Characteristic difference methods are suitable for solving convection dominated diffusion problems. They are generally first order accurate and have non physical oscillations. The quadratic monotone interpolation characteristic difference method is proposed to overcome these defects. The method is nonoscillatory, higher order accurate, and unconditionally stable. The difference equations are solved by the alternating group explicit (AGE) method which is specially suitable for parallel calculations. Simulation results show that the method not only eliminates numerical oscillations, but also has high precision. The new characteristic difference method can be used to successfully solve convection dominated diffusion problems.