Extensions of the meshless finite volume particle method (FVPM) for static and dynamic free-surface flows

The Finite Volume Particle Method (FVPM) is a meshless method that incorporates features of both Smoothed Particle Hydrodynamics and the Finite Volume Method. Here, two new formulations are presented which enhance its performance in simulation of free surface flows. One is a method for determining the velocity of the free surface, making use of a partial Riemann problem to analyse the flow between the particle barycentre and the geometric free surface. The second is a well-balanced formulation for gravity forces that enables hydrostatic equilibrium to be preserved exactly. Results are presented for hydrostatic, 1D impact, dambreak and deep-water standing wave test cases. Computations display convergence and good agreement with experimental data. The new methods recover exact hydrostatic equilibrium, improve robustness and reduce acoustic pressure fluctuations in dambreak flows, and reduce dissipation.