Numerically nonreflecting boundary and interface conditions for compressible flow and aeroacoustic computations

Accuratenonreecting orradiationboundaryconditionsareimportantforeffectivecomputation ofaeroacoustic and compressibleow problems. Theperformance of such boundary conditions is often degraded upon discretiza- tion of the equations with ® nite difference and time marching methods. In particular, poorly resolved, spurious sawtooth waves are generated at boundaries due to the dispersive nature of the ® nite difference approximation. These disturbances can lead to spurious self-sustained oscillations in theow (self-forcing), poor convergence to steady state, and long timeinstability ofthenumerics. Exact discretely nonreecting boundary closures (boundary conditionsforadownwindarti® cialboundary andanupwindphysicalboundary)arederived by considering aone- dimensional hyperbolic equation discretized with ® nite difference schemes and Runge± Kutta time advancements. The current methodology leads to stable local ® nite difference-like boundary closures, which are nonreecting to an essentially arbitrarily high order of accuracy. These conditions can also be applied at interfaces where there is a discontinuity in the wave speed (a shock) or where there is an abrupt change in the grid spacing. Compared to other boundary treatments, the present boundary and interface conditions can reduce spurious reected energy in the computational domain by many orders of magnitude.