ISSN:
0271-2091
Keywords:
convection-dominated diffusion equations
;
TVD schemes
;
antidiffusive schemes
;
flux limiter scheme
;
Engineering
;
Numerical Methods and Modeling
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
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.
Additional Material:
8 Ill.
Type of Medium:
Electronic Resource
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