RADIATION AND OUTFLOW BOUNDARY CONDITIONS FOR DIRECT COMPUTATION OF ACOUSTIC AND FLOW DISTURBANCES IN A NONUNIFORM MEAN FLOW

It is well known that Euler equations support small amplitude acoustic, vorticity and entropy waves. To perform high quality direct numerical simulations of flow generated noise problems, acoustic radiation boundary conditions are required along inflow boundaries. Along boundaries where the mean flow leaves the computation domain, outflow boundary conditions are needed to allow the acoustic, vorticity and entropy disturbances to exit the computation domain without significant reflection. A set of radiation and outflow boundary conditions for problems with nonuniform mean flows are developed in this work. Flow generated acoustic disturbances are usually many orders of magnitude smaller than that of the mean flow. To capture weak acoustic waves by direct computation (without first separating out the mean flow), the intensity of numerical noise generated by the numerical algorithm and the radiation and outflow boundary conditions (and the computer) must be extremely low. It is demonstrated by a test problem involving sound generation by an oscillatory source that weak acoustic waves with maximum velocity fluctuation of the order of 10⁻⁹ of the mean flow velocity can be computed accurately using the proposed radiation boundary conditions. The intensity of such acoustic waves is much smaller than the numerical error of the mean flow solution.