Journal
APPLIED NUMERICAL MATHEMATICS
Volume 56, Issue 5, Pages 589-607Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.apnum.2005.04.004
Keywords
conservation laws; multidimensional finite difference schemes; stability; Lax-Wendroff scheme
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In one and two spatial dimensions, Lax-Wendroff schemes provide second-order accurate optimally-stable dispersive conservation-form approximations to non-linear conservation laws. These approximations are an important ingredient in sophisticated simulation algorithms for conservation laws whose solutions are discontinuous. Straightforward generalization of these Lax-Wendroff schemes to three dimensions produces an approximation that is unconditionally unstable. However, some dimensionally-split schemes do provide second-order accurate optimally-stable approximations in 3D (and 2D), and there are sub-optimally-stable non-split Lax-Wendroff-type schemes in 3D. The main result of this paper is the creation of new Lax-Wendroff-type second-order accurate optimally-stable dispersive non-split scheme that is in conservation form. The scheme is created by using linear equivalence to transform a symmetrized dimensionally-split scheme (based on a one-dimensional Lax-Wendroff scheme) to conservation form. We then create both composite and hybrid schemes by combining the new scheme with the diffusive first-order accurate Lax-Friedrichs scheme. Codes based on these schemes perform well on difficult fluid flow problems. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.
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