Solid wall boundary conditions for computational aeroacoustics problems

It is known that the use of high-order finite 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. The large stencils associated with high-order schemes make the implementation of solid wall boundary conditions a non-trivial task. Several major difficulties in numerical enforcement of the solid wall boundary conditions are investigated and resolved. The research work includes: (a) Development of a Cartesian boundary treatment for acoustic wave scattering problems involving solid objects with curved surfaces; (b) Extension of the boundary treatment to include viscous effects. A sequence of direct numerical simulations involving solid objects of different geometries including those with sharp corners are performed to demonstrate the effectiveness of the proposed method.