351 IGPM.pdf        December 2012
TITLE A Finite Volume Evolution Galerkin Scheme for Acoustic Waves in Heterogeneous Media
AUTHORS Koottungal Revi Arun, Guoxian Chen, Sebastian Noelle
ABSTRACT In this paper, we present a numerical scheme for the propagation of acoustic waves in a heterogeneous medium in the context of the finite volume evolution Galerkin (FVEG) method (M. Lukáčová-Medviďová et al. J. Comput. Phys., 183:533–562, 2002). As a mathematical model we consider a wave equation system with space dependent wave-speed and impedance, which is used to study the wave propagation in a complex media. A main building block of our scheme is a genuinely multidimensional evolution operator based on the bicharacteristic theory of hyperbolic systems under the assumption of space dependent Jacobian matrices. We employ a novel approximation of the evolution operator, resulting from quadratures, in the flux evaluation stage of a finite volume scheme. The results of several numerical case studies clearly demonstrate the efficiency and robustness of the new FVEG scheme.
KEYWORDS heterogeneous media, acoustic waves, finite volume methods, evolution Galerkin scheme, hyperbolic conservation laws, bicharacteristics.
PUBLICATION AIMS series on applied mathematics 8,
439 - 446 (2014)