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

Arun, K.R. ; Kraft, M. ; Lukáčová-Medvid’ová, M. ; Prasad, Phoolan (2009) Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions Journal of Computational Physics, 228 (2). pp. 565-590. ISSN 0021-9991

[img]
Preview
PDF - Author Version
5MB

Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00219...

Related 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. Lukáčová-Medvid’ová, J. Saibertov’a, G. Warnecke, Finite volume evolution Galerkin methods for nonlinear hyperbolic systems, J. Comp. Phys. (2002) 183 533– 562; M. Lukáčová-Medvid’ová, 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:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Evolution Galerkin Scheme; Finite Volume Methods; Bicharacteristics; Wave Equation; Heterogeneous Media; Acoustic Waves
ID Code:37573
Deposited On:25 Apr 2011 10:20
Last Modified:17 May 2016 20:28

Repository Staff Only: item control page