On the filtering of acoustic components in weakly-compressible SPH simulations

The present paper is dedicated to the post-processing analysis of the time pressure signals when a weakly-compressible Smoothed Particle Hydrodynamics (SPH) model is used to simulate free-surface flows. Indeed, it is well known in literature that this particle model is characterized by the occurrence of high-frequency acoustic noise making the pressure signals unusable for engineering applications. This non-physical pressure noise is both linked to the weakly-compressible approach and to numerical inaccuracies. To reduce the latter, different enhanced SPH models have been developed in recent years. Nonetheless, even using accurate and stable SPH schemes when simulating water impacts, acoustic signals can be generated and, since the speed of sound used in the model is not the real one, these acoustic components need to be filtered in a suitable way. Indeed, for low Mach number regime the solution of the compressible Navier-Stokes equation can be decomposed in an incompressible solution plus an acoustic perturbation. In this work, a filtering technique based on Wavelet Transform is presented. In the proposed procedure the acoustic frequencies are individuated through a preliminary analysis which takes into account: the adopted speed of sound, the spatial resolutions and the fluid domain configuration. The filtering technique to remove the acoustic components is finally applied to several test-cases ranging from prototype problems to more practical applications such as a violent sloshing flow.