New formulation of Hardin-Pope equations for aeroacoustics

Predictions of aeroacoustic disturbances generated by low-speed unsteady flows can be obtained with the two-step method proposed by Hardin and Pope (Hardin, J. C., and Pope, S. D., "An Acoustic/Viscous Splitting Technique for Computational Aeroacoustics," Theoretical and Computational Fluid Dynamics, Vol. 6, No. 5-6, 1994, pp. 334-340). This method requires detailed information about the unsteady aerodynamic flowfield, which usually is obtained from a computational fluid dynamics solution. A new, conservative formulation of the equations governing acoustic disturbances is presented. The conservative form of the governing equations is obtained after application of a transformation of variables that produces a set of inhomogeneous equations similar to the conservation-law form of the compressible Euler equations. The source term of these equations depends only on the derivatives of the hydrodynamic variables. Explicit time marching is performed. A high-order accurate, upwind-biased numerical scheme is used for numerical solution of the conservative equations. The convective fluxes are evaluated using upwind-biased formulas and flux-vector splitting. Solutions are obtained for the acoustic flowfield generated by a corotating vortex pair. Computed results are compared with the analytic solution.