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Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions

Aruna, KR and Kraft, M and Lukacova-Medvidova, M and Prasad, Phoolan (2009) Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions. In: Journal Of Computational Physics, 228 (2). pp. 565-590.

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Official URL: http://dx.doi.org/10.1016/j.jcp.2008.10.004

Abstract

We present a generalization of the finite volume evolution Galerkin scheme [M. Lukacova-Medvid'ova,J. Saibertov'a, G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comp. Phys. (2002) 183 533-562; M. Luacova-Medvid'ova, K.W. Morton, G. Warnecke, Finite volume evolution Galerkin (FVEG) methods for hyperbolic problems, SIAM J. Sci. Comput. (2004) 26 1-30] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex systems. The finite volume evolution Galerkin (FVEG) method is a predictor-corrector method combining the finite volume corrector step with the evolutionary predictor step. In order to evolve fluxes along the cell interfaces we use multi-dimensional approximate evolution operator. The latter is constructed using the theory of bicharacteristics under the assumption of spatially dependent wave speeds. To approximate heterogeneous medium a staggered grid approach is used. Several numerical experiments for wave propagation with continuous as well as discontinuous wave speeds confirm the robustness and reliability of the new FVEG scheme.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to Elsevier.
Keywords: Evolution Galerkin scheme; Finite volume methods; Bicharacteristics; Wave equation; Heterogeneous media; Acoustic waves
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 11 Jun 2010 08:25
Last Modified: 19 Sep 2010 05:27
URI: http://eprints.iisc.ernet.in/id/eprint/19349

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