对流扩散方程的三阶迎风格式的数值摄动高精度重构  

Numerical perturbation higher accurate reconstruction Scheme of 3-UDS for convective-diffusion equation

作　　者：杨满叶[1,2] 舒适[1] 李明军[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105 [2]中国科学院力学研究所,北京100080

出　　处：《水动力学研究与进展（A辑）》2010年第3期307-315,共9页Chinese Journal of Hydrodynamics

基　　金：国家自然科学基金项目(10872204;10771178);国家自然科学基金委员会-中国工程物理研究院联合基金(10676031);教育部博士点基金(20070530003)

摘　　要：利用高智提出的数值摄动算法,把求解对流扩散方程常用三阶迎风格式(3-UDS)(粘性项和对流项分别用二阶中心格式和3-UDS离散)进行了高精度重构,包括使用离散单元内所有节点的全域重构和分别使用上下游节点的上下游重构,得到两类新的更高阶精度迎风差分格式,称为高的迎风差分格式(记作GUDS)。讨论了GUDS的数学性质,GUDS比原来的3-UDS精度显著提高;全域重构的GUDS和3-UDS均为条件稳定,一些上下游重构GUDS为绝对稳定。本文通过稳定性分析和四个算例(一维常系数、变系数、非线性及二维变系数对流扩散方程)的计算证实了GUDS的优良性质。上下游重构GUDS为避免在3-UDS中使用人工粘性提供了一条有效途径,适合于求解高Reynolds数线性和非线性问题。The discrete scheme of the convective-diffusion equation,in which the viscous and convective terms are discrete as second-order central and third-order upwind difference scheme（3UDS） separately,was reconstructed by using the numerical perturbation algorithm presented by Gao Zhi.The reconstruct methods have two,one is global reconstruction using all node-information in discrete element,the other is upstream and downstream reconstruction using separately upstream and downstream node-information in a discrete element.The two kinds of higher-order schemes called Gao＇s upwind difference schemes （GUDS,for braviety） were developed by using two reconstruct methods stated above.GUDS is so simple as 3UDS,but GUDS have more high accurate than 3UDS.Both global GUDS and 3UDS are conditional stable schemes,while some GUDS of upstream and downstream reconstruction are absolute stable schemes.Excellent properties of GUDS for the convective-diffusion equation were proved by analysis and four numerical tests.The results show that GUDS of upstream and downstream reconstruction provide a new effective way for 3UDS needing no artificial viscosity and are suitable for solving linear and nonlinear high Reynolds number problems.

关 键 词：高迎风差分格式 对流扩散方程 三阶迎风格式 数值摄动高精度重构 

分 类 号：O357.1[理学—流体力学]