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 numerica l simulations of flow generated noise problems, acoustic radiation bou ndary conditions are required along inflow boundaries. Along boundarie s where the mean flow leaves the computation domain, outflow boundary conditions are needed to allow the acoustic, vorticity and entropy dis turbances to exit the computation domain without significant reflectio n. A set of radiation and outflow boundary conditions for problems wit h nonuniform mean flows are developed in this work. Flow generated aco ustic disturbances are usually many orders of magnitude smaller than t hat of the mean flow. To capture weak acoustic waves by direct computa tion (without first separating out the mean how), the intensity of num erical noise generated by the numerical algorithm and the radiation an d outflow boundary conditions (and the computer) must be extremely low . It is demonstrated by a test problem involving sound generation by a n oscillatory source that weak acoustic waves with maximum velocity fl uctuation of the order of 10(-9) of the mean flow velocity can be comp uted accurately using the proposed radiation boundary conditions. The intensity of such acoustic waves is much smaller than the numerical er ror of the mean flow solution.