High-order accurate dual time-stepping algorithm for viscous aeroacoustic simulations

The field of computational aeroacoustics (CAA) has shown great promise in the solution of primarily inviscid noise generation and wave propagation problems that are governed by the Euler equations. The present research extends these ideas to the solution of the Navier-Stokes equations in multi-dimensions where the acoustic and flow fields may be influenced by viscous effects. In this paper, efficient acceleration techniques typical of explicit steady-state solvers are extended to time-accurate calculations. Stability restrictions based on the grid spacing are relaxed greatly with the implementation of a fully implicit time discretization. Some simplified problems that address the important issues of viscous calculations are investigated. A two-dimensional, Navier-Stokes code, written in Fortran 90 with the Message Passing Library (MPI) as a parallel implementation, is used to perform these calculations. As an example calculation, scattering of an acoustic source by a flat plate in the presence of a mean flow including a viscous boundary layer is presented.