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AN ACCURATE FINITE DIFFERENCE SCHEME FOR SOLVING CONVECTION‐DOMINATED DIFFUSION EQUATIONS
Author(s) -
Bruneau Ch. H.,
Fabrie P.,
Rasetarinera P.
Publication year - 1997
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19970130)24:2<169::aid-fld486>3.0.co;2-j
Subject(s) - flux limiter , interpolation (computer graphics) , mathematics , convection–diffusion equation , scheme (mathematics) , total variation diminishing , finite difference , diffusion , convection , term (time) , finite difference method , upwind scheme , mathematical analysis , mathematical optimization , computer science , mechanics , physics , discretization , thermodynamics , animation , computer graphics (images) , quantum mechanics
Approximating convection‐dominated diffusion equations requires a very accurate scheme for the convection term. The most famous is the method of backward characteristics, which is very precise when a good interpolation procedure is used. However, this method is difficult to implement in 2D or 3D. The goal of this paper is to show that it is possible to construct finite difference schemes almost as accurate as the method of characteristics. Starting from a family of second‐ and third‐ order Lax–Wendroff‐type schemes, a TVD and L ∞ ‐ stable scheme that is easy to implement in higher dimensions is constructed. Numerical tests are performed on various model problems whose solution is known and on classical problems. Comparisons with some other limiter schemes and the method of characteristics are discussed. © 1997 by John Wiley & Sons, Ltd.