Numerical Eulerian method for linearized gas dynamics in the high frequency regime

We study the propagation of an acoustic wave in a moving fluid in the high frequency regime. We calculate a high-frequency approximation of the solution of this problem using an Eulerianmethod. The model retained is a linearized Euler system around a mean fluid flow. For any regular mean flow, we derive a conservative transport equation for the geometrical optics approximation. We introduce the stretching matrix corresponding to this system, from which we deduce the geometrical spreading, key tool for computing the geometrical optics approximation. Finally, we construct and implement a numerical scheme in the Eulerian framework for the eikonal equation. This Eulerian formulation applies also for the transport equation on the stretching matrix. KeywordsHamilton-Jacobi equation; hyperbolic system; numerical scheme; asymptotic analysis; acoustic wave; high frequency regime. AMS Subject Classification 35B40; 35L50; 65N06; 76Q05. This work has been supported by EADS-Innovation Works through the funding of the PhD thesis of Y. Noumir.