A Perfectly Matched Layer absorbing boundary condition for linearized Euler equations with a non-uniform mean flow

Abstract

A Perfectly Matched Layer (PML) for linearized Euler equations with a parallel non-uniform mean flow is presented. The PML is formulated by utilizing a proper space–time transformation in its derivation so that in the transformed coordinates all dispersive waves supported by the non-uniform flow have consistent phase and group velocities. The space–time transformation is determined through a study of dispersion relations of all the linear waves. The proposed PML equations are applicable to both bounded and unbounded flows and given in unsplit physical variables. Furthermore, the stability of the PML is also considered. It is shown that the proposed PML is stable for a finite range of the absorption coefficient. Numerical examples that demonstrate the validity and effectiveness of PML as an absorbing boundary condition are presented.