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Preprint 2008-026

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

K.R. Arun, M. Kraft and M. Lukáčová-Medviďová

Abstract: We present a generalization of the finite volume evolution Galerkin scheme [doi:10.1006/jcph.2002.7207, doi:10.1137/S1064827502419439] \cite{jcp, sisc} 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.

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K.R. Arun
M. Kraft
M. Lukáčová-Medviďová
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; 2008-09-08.