A weakly compressible free-surface flow solver for liquid–gas systems using the volume-of-fluid approach

This paper presents a weakly compressible volume-of-fluid formulation for modelling immiscible high density ratio two-fluid flow under low Mach number conditions. This follows findings of experimental analyses that concluded the compressibility of the gas has a noteworthy effect on predicted pressure loads in liquid–gas flow in certain instances. With the aim of providing a more accurate numerical representation of dynamic two-fluid flow, the solver is subsequently extended to account for variations in gas densities. A set of governing equations is proposed, which accounts for the compressible properties of the gas phase in a manner which allows for a computationally efficient numerical simulation. Furthermore, the governing equations are numerically expressed so that they allow for large variations in the material properties, without introducing notable non-physical oscillations over the interface. For the discretisation of the governing equations an edge-based vertex-centred finite volume approach is followed. The developed solver is applied to various test cases and demonstrated to be efficient and accurate.