Non-reflecting Boundary Conditions for Wave Propagation Problems

We consider two aspects of non-reflecting boundary conditions for wave propagation problems. First we evaluate a proposed Perfectly Matched Layer (PML) method for the simulation of advective acoustics. It is shown that the proposed PML becomes unstable for a certain combination of parameters. A stabilizing procedure is proposed and implemented. By numerical experiments the performance of the PML for a problem with nonuniform flow is investigated. Further the performance for different types of waves, vorticity and sound waves, are investigated. The second aspect concerns spurious waves, which are introduced by any discretization procedure. We construct discrete boundary conditions, that are nonreflecting for both physical and spurious waves, when combined with a fourth order accurate explicit discretization of one-way wave equations. The boundary condition is shown to be GKS-stable. The boundary conditions are extended to hyperbolic systems in two space dimensions, by combining exact continuous non-reflecting boundary conditions and the one dimensional discretely non-reflecting boundary condition. The resulting boundary condition is localized by the standard Padé approximation. Numerical experiments reveal that the resulting method suffers from boundary instabilities. Analysis of a related continuous problem suggests that the discrete boundary condition can be stabilized by adding tangential viscosity at the boundary. For the lowest order Padé approximation we are able to stabilize the discrete boundary condition. ISBN 91-7283-628-8 • TRITA-NA-0326 • ISSN 0348-2952 • ISRN KTH/NA/R--03/26--SE