Search

The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization and localization at the boundaries based on these variables. The proposed boundary conditions are applied through a penalty procedure, thus ensuring correct behavior of the scheme as the Reynolds number tends to infinity. The versatility of this method is demonstrated for the problem of a compressible now past a circular cylinder.

We investigate the long time behavior of two unsplit PML methods for the absorption of electromagnetic waves. Computations indicate that both methods suffer from a temporal instability after the fields reach a quiescent state. The analysis reveals that the source of the instability is the undifferentiated terms of the PML equations and that it is associated with a degeneracy of the quiescent systems of equations. This highlights why the instability occurs in special cases only and suggests a remedy to stabilize the PML by removing the degeneracy. Computational results confirm the stability of the modified equations and is used to address the efficacy of the modified schemes for absorbing waves.