Nonre ecting Boundary Conditions for Linear Hyperbolic Systems 1

Many compressible ow and aeroacoustic computations rely on accurate nonre ecting or radiation boundary conditions. When the equations and boundary conditions are discretized using a nite-di erence scheme, the dispersive nature of the discretized equations can lead to spurious numerical re ections not seen in the continuous boundary value problem. Here we construct discretely nonre ecting boundary conditions, which account for the particular nite-di erence scheme used, and are designed to minimize these spurious numerical re ections. Stable boundary conditions that are local and nonre ecting to arbitrarily high order of accuracy are obtained, and test cases are presented for the linearized Euler equations. For the cases presented, re ections for a pressure pulse leaving the boundary are reduced by up to two orders of magnitude over typical ad hoc closures, and for a vorticity pulse, re ections are reduced by up to four orders of magnitude.