半自适应网格方法及其应用

Semi-adaptive Grid Method and its Applications

本文发展了一种简单而有效的所谓半自适应网格方法，该方法的一个特点是所有的计算均在物理平面上完成。这种半自适应方法已被成功地应用于定常和非定常一维二维对流扩散方程初边值问题的数值解，与存在精确解的结果比较表明，半自适应网格方法的结果具有很少的数值耗散，精度较好，与通常的差分方法比大约增加一倍多一点的计算时间，与变分或微分形式的自适应网格方法相比，大大减少了计算工作量。

A simple and efficient so called semi-adaptive grid method has been developed in the paper. One speciality of this method is that all numerical calculation are carried out on the physical plane. This semi-adaptive grid method has been successfully applied to solve the one and two dimensional steady or unsteady initial boundary value problems of convection-diffusion equations. The comparison with existing exact solution illustrates that semi-adaptive grid method has high accuracy and a little numerical diffusion. The computation time is much less than that of using the variational or differential formulation, The computation time is about one times of using ordinary finite difference method.