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

  • Authors:

  • K. R. Arun;M. Kraft;M. Lukáčová-Medvid'ová;Phoolan Prasad

  • Affiliations:

  • Indian Institute of Science, Bangalore, India;Institute of Numerical Simulation, Hamburg University of Technology, Schwarzenbergstrasse 95, Hamburg 21073, Germany;Institute of Numerical Simulation, Hamburg University of Technology, Schwarzenbergstrasse 95, Hamburg 21073, Germany;Indian Institute of Science, Bangalore, India

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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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. Lukacova-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.