Perfectly Matched Layers for the Convected Helmholtz Equation

Abstract

Perfectly Matched Layers (PML), introduced by Bérenger [3] in order to design efficient numerical absorbing boundary conditions for Maxwell’s equations in unbounded domains, have been used for the resolution in the time domain of the linearized Euler equations [7, 9, 1] which modelize the acoustic propagation in presence of flow. In that case, it has been observed that perfectly matched layers can lead to instabilities, produced by waves whose phase and group velocities have opposite signs [9] (see [2] for a general analysis of this phenomenon). This has given rise to several models for time domain applications [1, 6].