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 the asymptotic approximation of the solution, around a mean flow, of this problem using an Eulerian method. By introducing the stretching matrix (deformation tensor for the geometrical optics rays) of the linearized Euler system, we deduce the geometrical spreading. This quantity is the key tool for computing the leading order term of the asymptotic expansion thanks to a conservation equation along the group velocity. The main contribution is to construct and implement a numerical scheme in the Eulerian framework for the eikonal equation and for the transport equation on the stretching matrix. We present numerical results for several test cases to study the convergence and validate our approach.