Perfectly Matched Layer as an Absorbing Boundary Condition for the Linearized Euler Equations in Open and Ducted Domains

Abstract

Recently, perfectly matched layer (PML) as an absorbing boundary condition has found widespread applications. The idea was first introduced by Berenger for electromagnetic waves computations. In this paper, it is shown that the PML equations for the linearized Euler equations support unstable solutions when the mean flow has a component normal to the layer. To suppress such unstable solutions so as to render the PML concept useful for this class of problems, it is proposed that artificial selective damping terms be added to the discretized PML equations. It is demonstrated that with a proper choice of artificial mesh Reynolds number, the PML equations can be made stable. Numerical examples are provided to illustrate that the stabilized PML performs well as an absorbing boundary condition. In a ducted environment, the wave modes are dispersive. It will be shown that in the presence of a mean flow the group velocity and phase velocity of these modes can have opposite signs. This results in a band of transmitted waves in the PML to be spatially amplifying instead of evanescent. Thus in a confined environment, PML may not be suitable as an absorbing boundary condition unless there is no mean flow.