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.