Perfectly Matched Layer as an Absorbing Boundary Condition

Perfectly matched layer (PML) was invented by Berenger (1994,1996) as an absorb­ing boundary condition for computational electromagnetics. The idea is to enclose a computational domain by a PML. In the PML, a modified set of governing equations are used. The modified equations, as designed, have the unusual characteristics that, when an outgoing disturbance impinges on the interface between the computational domain and the absorbing layer, no wave is reflected back. In other words, all out­going disturbances are transmitted into the absorbing layer where they are damped out.

Hu (1996) was the first to apply PML successfully to aeroacoustic problems governed by the linearized Euler equations. In the beginning, the linearization was done over a uniform mean flow. Recently, Hu (2005) had extended his work to nonuniform mean flow. Tam et al. (1998) analyzed the original version of the PML equations. They pointed out that those equations supported spatially growing unsta­ble solutions. This is because, in the presence of a mean flow, the PML equations give rise to dispersive waves. In the original version of PML, a small band of these waves has phase velocity in the opposite direction to the group velocity. Spatial damping in the PML is associated with the direction of the phase velocity. As a result, these waves grow in amplitude as they propagate across the PML instead of being damped. Hu (2001,2004) has since resolved this instability problem. In this chapter, the more recent PML equations developed by Hu are presented and analyzed.