Application of background pressure with kinematic criterion for free surface extension to suppress non-physical voids in the finite volume particle method

Lagrangian particle methods such as smoothed particle hydrodynamics (SPH) and the finite volume particle method (FVPM) can suffer from non-physical voids in the spatial discretisation, due to the inability of numerical particles to deform as continuum fluid elements can. It is known that the situation can be improved for wall-bounded flows in SPH by adding a uniform background pressure to ensure positive absolute pressure everywhere. In this article, we investigate the application of background pressure in FVPM, and show that numerical voids grow under negative pressure and collapse under positive pressure. To use this technique in free-surface flow, however, the background pressure must be applied as an atmospheric pressure at the free surface. A kinematic criterion for free surface extension (KCFSE) to differentiate physical free surfaces from new numerical voids has been developed, supplementing the inherent capability of FVPM to identify free-surface particles robustly. The novel method enables background pressure to be applied at physical free surfaces and throughout the fluid, but not in non-physical voids, facilitating the suppression of such spurious voids. The KCFSE is validated for a translating square cylinder inside a rectangular numerical domain, with and without a free surface, and liquid in an oscillating rectangular tank.