Numerically nonreflecting boundary conditions for multidimensional aeroacoustic computations

Many compressible flow and aeroacoustic computations rely on accurate nonreflecting or radiation boundary conditions. When the equations and boundary conditions are discretized using a finite- difference scheme, the dispersive nature of the discretized equations can lead to spurious numerical reflections not seen in the continuous boundary value problem. These reflections can lead to poor convergence to a stationary state, and can lead to self-forcing of flows. We have constructed numerically nonreflecting boundary conditions which account for the particular finite-difference scheme used, and are designed to minimize these spurious numerical reflections. These extend our earlier work on one- dimensional boundary conditions to the multidimensional case. Stable boundary conditions which are nonreflecting to arbitrarily high-order-of-accuracy are obtained. Various test cases are presented which show excellent results.