2007•International Journal for Numerical Methods in FluidsRequires access

RCM‐TVD hybrid scheme for hyperbolic conservation laws

Yousef Hashem Zahran

Abstract

Abstract We describe a hybrid method for the solution of hyperbolic conservation laws. A third‐order total variation diminishing (TVD) finite difference scheme is conjugated with a random choice method (RCM) in a grid‐based adaptive way. An efficient multi‐resolution technique is used to detect the high gradient regions of the numerical solution in order to capture the shock with RCM while the smooth regions are computed with the more efficient TVD scheme. The hybrid scheme captures correctly the discontinuities of the solution and saves CPU time. Numerical experiments with one‐ and two‐dimensional problems are presented. Copyright © 2007 John Wiley & Sons, Ltd.

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Key concepts: Conservation law, Total variation diminishing, Classification of discontinuities, Mathematics, Grid, Scheme (mathematics), Applied mathematics, Finite difference