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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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|
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