二维对流扩散方程的二阶精度特征差分格式

A Family of Second Order Characteristic Difference Schemes for Two-dimensional Convection-diffusion Equations

针对二维对流扩散方程提出了几类二阶精度特征差分格式,给出了这些格式形成的线性代数方程组可解的充分条件,分析证明了这些格式按离散L2模是二阶收敛的。最后,具体算例表明这些格式对于对流扩散方程有良好的计算效果。

This paper presents a family of second order characteristic difference schemes for two- dimensional convection-diffusion equations. It gives suffcient conditions for solving the linear systems which formed by these schemes, and proves that the methods converge in discrete L2 norm to the solution of the convection-diffusion equation with second order accuracy. Finally, numerical example shows that these schemes can be used to solve convection-diffusion equations effectively.