The characteristic finite difference streamline diffusion method for convection-dominated diffusion problems

被引：35
作者：
Qian, Lingzhi [1 ,2 ]
Feng, Xinlong [1 ]
He, Yinnian [1 ,3 ]
机构：
[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Peoples R China
[2] Shihezi Univ, Sch Sci, Dept Math, Shihezi 832003, Peoples R China
[3] Xi An Jiao Tong Univ, Fac Sci, Xian 710049, Peoples R China
来源：
APPLIED MATHEMATICAL MODELLING | 2012年 / 36卷 / 02期
基金：
中国博士后科学基金; 国家高技术研究发展计划(863计划); 中国国家自然科学基金;
关键词：
Convection-dominated diffusion equation; Characteristics; Finite difference streamline diffusion method; Stability analysis; Error estimate; NAVIER-STOKES EQUATIONS; VOLUME ELEMENT METHOD; SCHEME;
D O I：
10.1016/j.apm.2011.07.034
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper, we consider the characteristic finite difference streamline diffusion method for two-dimensional convection-dominated diffusion problems. The scheme is combined the method of characteristics with the finite difference streamline diffusion (FDSD) method to create the characteristic FDSD (C-FDSD) procedures. Stability analysis and error estimate of the C-FDSD method are deduced. The scheme not only realizes the purpose of lowering the time-truncation error, using larger time step for solving the convection-dominated diffusion problems, but also keeps the favorable stability and high precision of the FDSD method. Finally, numerical experiments are presented to illustrate the availability of the scheme. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：561 / 572
页数：12
相关论文
共 36 条
[1]  
Adams A., 2003, Sobolev Spaces, V140
[2]  
[Anonymous], E W J NUMER MATH
[3]  
[Anonymous], 2002, TEXTS APPL MATH
[4]  
BABA K, 1981, RAIRO-ANAL NUMER-NUM, V15, P3
[5]   STREAMLINE UPWIND PETROV-GALERKIN FORMULATIONS FOR CONVECTION DOMINATED FLOWS WITH PARTICULAR EMPHASIS ON THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS [J].
BROOKS, AN ;
HUGHES, TJR .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1982, 32 (1-3) :199-259
[6]  
CHEN L, 2005, RECENT ADV ADAPTIVE, V383, P236
[7]  
Chen Z., 2005, Finite Element Methods and Their Applications
[8]   NUMERICAL-METHODS FOR CONVECTION-DOMINATED DIFFUSION-PROBLEMS BASED ON COMBINING THE METHOD OF CHARACTERISTICS WITH FINITE-ELEMENT OR FINITE-DIFFERENCE PROCEDURES [J].
DOUGLAS, J ;
RUSSELL, TF .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1982, 19 (05) :871-885
[9]  
ERIKSSON K, 1993, MATH COMPUT, V60, P167, DOI 10.1090/S0025-5718-1993-1149289-9
[10]   The characteristic finite volume element method for the nonlinear convection-dominated diffusion problem [J].
Gao, Fuzheng ;
Yuan, Yirang .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (01) :71-81
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