NUMERICALLY NONREFLECTING BOUNDARY AND INTERFACE CONDITIONS FOR COMPRESSIBLE FLOW AND AEROACOUSTIC COMPUTATIONS

Accurate nonreflecting or radiation boundary conditions are important for effective computation of aeroacoustic and compressible flow proble ms. The performance of such boundary conditions is often degraded upon discretization of the equations with finite difference and time march ing methods. In particular, poorly resolved, spurious sawtooth waves a re generated at boundaries due to the dispersive nature of the finite difference approximation. These disturbances can lead to spurious self -sustained oscillations in the flow (self-forcing), poor convergence t o steady state, and long time instability of the numerics. Exact discr etely nonreflecting boundary closures (boundary conditions for a downw ind artificial boundary and an upwind physical boundary) are derived b y considering a one-dimensional hyperbolic equation discretized with f inite difference schemes and Runge-Kutta time advancements. The curren t methodology leads to stable local finite difference-like boundary cl osures, which are nonreflecting to an essentially arbitrarily high ord er of accuracy. These conditions can also be applied at interfaces whe re 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 t reatments, the present boundary and interface conditions can reduce sp urious reflected energy in the computational domain by many orders of magnitude.