A collocated grid finite volume method for aeroacoustic computations of low-speed flows

A numerical algorithm for simulation of acoustic noise generation, based on collocated grids, is described. The approach, that was originally developed using a viscous/inviscid decomposition technique, involves two steps comprising a viscous incompressible flow part and an inviscid or viscous acoustic part. On collocated grids the inviscid solution is found to be mesh dependent due to unavoidable extrapolations of the acoustic pressure and density at walls, differing from the case on staggered grids where no extrapolation is needed. The situation is most pronounced when a sharp body is considered. A viscous acoustic algorithm is proposed to overcome the difficulty. Numerical computations of flows past a circular cylinder and a NACA 0015 airfoil show that a viscous/viscous coupling is more natural and gives excellent results as compared to those obtained in previous computations based on viscous/inviscid coupling on staggered grids. The model is applied to the problem of an airfoil exposed to a gust and results are compared to the numerical results of Lockard and Morris [AIAA J. 36(6) (1998) 907].