On perfectly matched layer as an absorbing boundary condition

Abstract

A Perfectly Absorbing Technique (PAT) is proposed for numerical solutions of the Euler equations. This technique follows the recent studies of Perfectly Matched Layer (PML) as absorbing boundary conditions. In the present paper, we construct the Perfectly Matched Layer equations for linear as well as non-linear Euler equations as an absorbing boundary condition. Plane wave solutions and propagation properties are analyzed for a uniform flow in an arbitrary direction. It is shown that the proposed PML equations are capable of absorbing the out-going acoustic, vorticity and entropy waves at numerical boundaries without reflection (theoretically) for any angle of incidence and frequency of the wave. The absorption rate is also independent of the wave frequency/wavelength. The PML equations are then extended to non-uniform mean flows. Moreover, by introducing a mean flow, PML equations for nonlinear Euler equations are constructed. The pseudo mean flow needs not to be an accurate prediction of the actual mean steady flow. Consequently, it becomes possible to apply the PML equations without the exact mean flow being available. Numerical examples that demonstrate the validity of the proposed absorbing boundary conditions are presented.