西北师范大学学报（自然科学版）2018，Vol.54Issue(2)：13-20,8.DOI:10.16783/j.cnki.nwnuz.2018.02.003
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
摘要
Abstract
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Key words
high order compact difference scheme/adaptive mesh/convection diffusion equation/boundary layer problems分类
数理科学引用本文复制引用
袁冬芳,曹富军,葛永斌..边界层对流扩散方程在自适应网格上的高精度紧致格式[J].西北师范大学学报（自然科学版）,2018,54(2):13-20,8.基金项目
国家自然科学基金资助项目(11361045) （11361045）
内蒙古自治区高等学校科学研究项目(NJZZ18140) （NJZZ18140）
内蒙古自然科学基金资助项目(2017MS(LH)0105) （2017MS(LH）
内蒙古科技大学校内创新基金资助项目(2014QDL004,2015QDL19) （2014QDL004,2015QDL19）
