Compressible air flow through a collapsing liquid cavity

We present a multiscale approach to simulate the impact of a solid object on a liquid surface: upon impact a thin liquid sheet is thrown upwards all around the rim of the impactor while in its wake a large surface cavity forms. Under the influence of hydrostatic pressure the cavity immediately starts to collapse and eventually closes in a single point from which a thin, needle-like jet is ejected. Existing numerical treatments of liquid impact either consider the surrounding air as an incompressible fluid or neglect air effects altogether. In contrast, our approach couples a boundary-integral method for the liquid with a Roe scheme for the gas domain and is thus able to handle the fully \emph{compressible} gas stream that is pushed out of the collapsing impact cavity. Taking into account air compressibility is crucial, since, as we show in this work, the impact crater collapses so violently that the air flow through the cavity neck attains supersonic velocities already at cavity diameters larger than 1 mm. Our computational results are validated through corresponding experimental data.