一种新的用于对流─扩散问题的差分格式

A New Finite Difference Formulation for Convection-Diffusion Equations

通过对３种常见坐标系中一维对流─扩散问题的分析，提出了一种新的差分格式．该格式具有目前普遍采用的幂律格式的一切优点，且比幂律格式更加简捷便于应用．它不采幂律格式那样，对不同的坐标系差分方程的系数具有不同的表达式，而是可以直接用于非直角坐标系．所以本文所提格式无疑是一种值得推广的新的用于对流扩散问题数值计算的差分格式．

A new finite difference formulation is developped based on the analytical solution of the one-dimensional convection-diffusion problem in both rectangular and non-rectangular coordinates. The new formulation is simpler, more convenient to use for non-rectangular coordinate problems compared with the widely-used power-law scheme. And it has all the advantages of power-law scheme. Examples for comparisons are also presented.