A semi-implicit immersed boundary method for simulating viscous flow-induced sound with moving boundaries

Abstract In this paper, a semi-implicit immersed boundary body force model is derived from the compressible Navier–Stokes equations, to directly predict the viscous flow-induced sound from moving objects on a fixed Cartesian grid. To overcome the conflict of grid quality with efficiency in simulating moving-boundary problems with high-order computational aeroacoustics methods, a prediction–correction technique is utilized. This accurately satisfies no-slip wall boundary conditions at every time step without any feedback treatment. A particular contribution of the work is the introduction of a numerical model equation to analyze the body force convergence. This is useful to pre-evaluate the generated Cartesian and body-surface grids. Several benchmark aeroacoustic problems are simulated to validate the present model. Results show that the unsteady force and far-field sound directivity agree well with the previous direct numerical simulation results. The work further suggests that the developed body force model/CAA methods are capable of predicting interaction noise, especially those associated with oscillating multiple objects.