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

作　　者：薛文强[1] 兰斌[1] 葛永斌[1] 

机构地区：[1]宁夏大学数学计算机学院,宁夏银川750021

出　　处：《西北师范大学学报（自然科学版）》2013年第4期16-24,33,共10页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11061025);霍英东教育基金会高等院校青年教师基金资助项目(121105);宁夏自然科学基金资助项目(NZ12123);宁夏大学自然科学基金资助项目(2R1120)

摘　　要：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.

关 键 词：一维定常对流扩散方程 非均匀网格 高阶紧致差分格式 边界层问题 

分 类 号：O241.82[理学—计算数学]