Composite Centered Schemes for Multidimensional Conservation Laws
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BibTeX
@MISC{Liska_compositecentered,
author = {Richard Liska and Burton Wendroff},
title = {Composite Centered Schemes for Multidimensional Conservation Laws},
year = {}
}
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Abstract
. The oscillations of a centered second order finite difference scheme and the excessive diffusion of a first order centered scheme can be overcome by global composition of the two, that is by performing cycles consisting of several time steps of the second order method followed by one step of the diffusive method. We show the effectiveness of this approach on some test problems in two and three dimensions. 1. Introduction For a system of conservation laws U t = f x (U ), it is well known that the LaxWendroff (LW) finite difference scheme produces oscillations behind shock waves while the Lax-Friedrichs (LF) method is excessively diffusive, smearing out the shocks more than is usually acceptable. Simple two-step versions of both schemes are defined as follows. For both schemes the first half step defines new values on a staggered dual grid as U n+1=2 i+1=2 = 1 2 [U n i + U n i+1 ] + \Deltat 2\Deltax [f(U n i+1 ) \Gamma f(U n i )]: (1) The second half step of the LF scheme is gi...
