Cartesian Boundary Treatment of Curved Walls for High-Order Computational Aeroacoustics Schemes

Abstract

It is known that the use of high-order central difference schemes on a Cartesian grid is preferable for the computation of acoustic wave propagation problems. Those schemes tend to be less dispersive and dissipative than most other types of schemes. They are also more capable of providing an accurate wave speed. A Cartesian boundary treatment for problems involving the scattering of acoustic waves by solid objects with curved boundary surfaces, designed to be used in conjunction with such high-order central difference schemes, is proposed. The development of this method is based on the observation that a solid wall actually exerts a pressure force on the fluid to keep it from flowing across the wall surface. In this method, ghost values of pressure are introduced at mesh points adjacent to the solid boundary inside the object. The ghost values are then chosen so that the solid wall boundary condition is satisfied. The method is also applicable to objects with sharp corners. Numerical examples are provided.