High-Order Radiation Boundary Conditions for the Convective Wave Equation in Exterior Domains

Abstract

We construct and apply radiation boundary conditions of arbitrary order for wave propagation with subsonic convection in exterior domains. The conditions generalize those we constructed earlier for the isotropic wave equation. As in the well-known work of Bayliss and Turkel, the construction is based on the progressive wave (or multipole) expansion of outgoing solutions. Using auxiliary functions defined only on the artificial boundary, problems associated with the use of high-order derivatives, as in the original Bayliss-Turkel formulation, are avoided. The order of the conditions is thus increased simply by using more auxiliary variables. By generalizing to the convective case, we have developed conditions which can be used in aeroacoustics applications whenever the Euler equations linearized about a uniform flow are sufficiently accurate in the far field. Numerical experiments in two space dimensions are presented to illustrate the stability and accuracy of the proposed technique.