Stabilized Local Non-reflecting Boundary Conditions for High Order Methods

Using the framework introduced by Rowley and Colonius [14] we construct a dis-cretely non-reflecting boundary condition for the one-way wave equation spatially discretized with an explicit fourth order centered difference scheme. The boundary condition, which can be extended to arbitrary order accuracy, is shown to be GKS-stable. We continue by deriving discretely non-reflecting boundary conditions for systems in two dimensions using the results for the scalar one dimensional case