网格Peclet数和网格尺寸对对流扩散方程差分格式精度的影响

用泰勒级数展开法对对流扩散方程中的扩散项进行了理论分析，从而证明对于给定的差分格式，不仅网格Ｐｅｃｌｅｔ数不能任意选取，而且网格尺寸也不能随意设定。用四种格式对一维有源对流扩散方程进行了计算，结果表明网格尺寸对差分格式精度的影响比网格Ｐｅｃｌｅｔ数更明显。为了得到真实可靠的结果，所用差分格式的阶数愈高，相应的网格尺寸就必须愈小。二阶以上的高精度迎风差分格式与二阶迎风格式相比，并无明显的优势，建议一般不必要采用二阶以上的高精度差分格式。

EFFECTS OF GRID PECLET NUMBER AND GRID SIZE ON ACCURACY OF FINITE-DIFFERENCE FORMULATIONS OF CONVECTION\|DIFFUSION EQUATIONS

A Taylor series analysis of the convection terms in convection diffusion equations is presented. A simple one dimensional convection diffusion equation with source terms was solved numerically by the use of four different formulations. The results show that neither the grid Peclet number nor the grid size can be chosen independently for the given difference formulation. The grid size has stronger effects on the accuracy of a formulation than the grid Peclet number. To get an acceptable physically true result, the higher the order of a formulation is, the smaller the required grid size is. The higher than second order formulations do not work anything better than the second order upwinding formulation. Therefore, the second order upwinding formulation is recommended for numerical modelling of convection diffusion equations.