On Absorbing Boundary Conditions for Linearized Euler Equations by a Perfectly Matched Layer

Recently, Berenger introduced a Perfectly Matched Layer (PML) technique for absorbing electromagnetic waves. In the present paper, a perfectly matched layer is proposed for absorbing out-going two-dimensional waves in a uniform mean ow, governed by linearized Euler equations. It is well known that the linearized Euler equations support acoustic waves, which travel with the speed of sound relative to the mean ow, and vorticity and entropy waves, which travel with the mean ow. The PML equations to be used at a region adjacent to the arti cial boundary for absorbing these linear waves are de ned. Plane wave solutions to the PML equations are developed and wave propagation and absorption properties are given. It is shown that the theoretical re ection coe cients at an interface between the Euler and PML domains are zero, independent of the angle of incidence and frequency of the waves. As such, the present study points out a possible alternative approach for absorbing out-going waves of the Euler equations with little or no re ection in computation. Numerical examples that demonstrate the validity of the proposed PML equations are also presented. This work was supported by the National Aeronautics and Space Administration under NASA contract NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23681, USA. This work was also supported by a summer research fellowship of Old Dominion University, Norfolk, VA 23529.