边界层对流扩散方程在自适应网格上的高精度紧致格式  

High order compact difference scheme on adaptive mesh for convection-diffusion problems with boundary layers

作　　者：袁冬芳 曹富军 葛永斌 YUAN Dong-fang;CAO Fu-jun;GE Yong-bin(School of Sciences,Inner Mongolia University of Science and Technology,Baotou 014010,Inner Mongolia,China;School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,Ningxia,China)

机构地区：[1]内蒙古科技大学理学院,内蒙古包头014010 [2]宁夏大学数学统计学院,宁夏银川750021

出　　处：《西北师范大学学报（自然科学版）》2018年第2期13-20,共8页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11361045);内蒙古自治区高等学校科学研究项目(NJZZ18140);内蒙古自然科学基金资助项目(2017MS(LH)0105);内蒙古科技大学校内创新基金资助项目(2014QDL004;2015QDL19)

摘　　要：对流扩散方程在非均匀网格上的高精度紧致格式具有精度高、模板小等优势,然而现有方法往往需要事先指定边界层或大梯度的位置,利用网格分布函数生成非均匀网格并调整网格分布参数,这严重影响方法的适用性.本文提出了一种在二维计算区域上生成正交网格的自适应方法,根据物理解的特征对网格的分布进行自适应调整,并结合非均匀网格上的高精度紧致格式对一维及二维边界层对流扩散问题进行求解.数值结果表明,自适应网格方法结合高阶紧致格式可以有效求解边界层问题,提高数值解的精度,减少计算所需的网格和计算量.The high order compact scheme on non-uniform grid for the convection diffusion equations has been widely studied because of its advantages of high accuracy and small stencil.However,the existing methods need to specify the position of boundary layer or large gradient in advance,and then apply the grid distribution functions to generate non-uniform grid and adjust the grid distribution parameters,which severely affect the applicability of the method.To overcome this deficiency,an adaptive mesh method is proposed which adaptively generates orthogonal non-uniform mesh for 2D rectangular computational domain according to the physical solution.The method combined with the HOC difference scheme on non-uniform grid is used to solve the 1D and 2D convection diffusion problems with boundary layers.The numerical results show that the presented method can effectively solve the problem with boundary layers,and improve the accuracy of the numerical solution and reduce the cost of computation.

关 键 词：高精度紧致格式 自适应网格 对流扩散方程 边界层问题 

分 类 号：O241.82[理学—计算数学]