一维定常对流扩散方程非均匀网格上的高阶紧致差分格式

A high-order compact difference scheme for solving the 1D steady convection diffusion equation on nonuniform grids

基于泰勒级数展开法提出了求解一维定常对流扩散方程非均匀网格上的高精度紧致差分格式,该格式具有3～4阶精度.通过对边界层和大梯度问题的数值实验,验证了该方法的精确性和有效性.与中心差分格式和其它几种格式的计算结果进行比较,结果表明,本文格式的计算结果要比已有的几种格式的计算结果更为精确.

A high-order compact difference scheme for solving the one dimensional（1D） steady convection diffusion equation on nonuniform grids is proposed based on Taylor series expansion. The accuracy of the scheme is the third- to fourth-order. Numerical experiments for some problems with boundary layers are conducted to validate the accuracy and the effectiveness of the present method. By comparing the computed results of the present scheme with that of the central difference scheme and the others schemes in the literature, it is found that the results computed by the present method is more accurate than that computed by some existed methods.