Numerically nonreflecting boundary and interface conditions

Abstract

Accurate nonreflecting or radiation boundary conditions are important for effective computation of aeroacoustic and compressible flow problems. In the present work, exact 'discretely nonreflecting boundary closures are derived by considering a one dimensional hyperbolic equation discretized with finite difference schemes and Runge-Kutta time advancements. The current methodology leads to stable local finite-difference-like boundary closures which are nonreflecting 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 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 reflected energy in the computational domain by many orders of magnitude.