Towards a monotonicity-preserving inviscid wall boundary condition for aeroacoustics

This paper presents an extension of the Tam and Dong solid wall boundary condition that combines the established non-penetration physical condition with a further restriction on the wall-normal velocity gradient. This results in a wall boundary condition in the form of a second-order partial differential equation which is satisfied analytically by fully reflecting acoustic waves and is monotonicity preserving in problems with a dominant near-boundary acoustic pressure distribution. With the extended wall boundary condition discretized to second-order spatial accuracy, tests on the wall reflection of a two-dimensional Gaussian pulse show that this condition suppresses the high wavenumber spurious numerical waves from the more conventional v = 0 formulation. This result is obtained using a compact finite-difference time-marching scheme that is sixth-order accurate in space and fourth-order accurate in time without the use of high-order filters applied to the computational domain interior. Copyright © 2009 by A. Rona.