A General Perfectly Matched Layer Model for Hyperbolic-Parabolic Systems

This paper describes a very general absorbing layer model for hyperbolic-parabolic systems of partial differential equations. For linear systems with constant coefficients it is shown that the model possesses the perfect matching property, i.e., it is a perfectly matched layer (PML). The model is applied to two linear systems: a linear wave equation with a viscous damping term and the linearized Navier–Stokes equations. The resulting perfectly matched layer for the viscous wave equation is proved to be stable. The paper also presents how the model can be used to construct an absorbing layer for the full compressible Navier–Stokes equations. For all three applications, numerical experiments are presented. Especially for the linear problems, the results are very promising. In one experiment, where the performance of a “hyperbolic PML” and the new hyperbolic-parabolic PML is compared for a hyperbolic-parabolic system, an improvement of six orders of magnitude is observed. For the compressible Navier–Stokes equations results obtained with the presented layer are competitive with existing methods.