Upwind Scheme for Acoustic Disturbances Generated by Low-Speed Flows
Computation of acoustic disturbances generated by unsteady, low-speed flows, such as flows including vortices and shear layers, can be obtained by a recently proposed two-step method. This method requires a hydrodynamic field solution and obtains the acoustic field from the perturbed, inviscid, compressible flow equations. A numerical method for the solution of the equations governing the acoustic field is presented. The primitive variable form of the governing equations is used for the numerical solution. Time integration is performed with a fourth-order, Runge-Kutta method. Discretization of the primitive variables space derivatives is obtained with a high-order, upwind-biased numerical scheme. Upwinding of these convective fluxes is performed according to the eigenvalue sign of the coefficient matrices. Nonreflecting boundary conditions are applied to properly convect outgoing waves away from the computational domain. Solutions are obtained for the acoustic field generated by a pair of corotating point vortices. Computed results are compared with the existing analytic solution for the sound field.