A Finite Volume Evolution Galerkin Scheme for Acoustic Waves in Heterogeneous Media

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-Medvid’ová 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.