Simulation of Free Surface Compressible Flows Via a Two Fluid Model

TL;DR

This paper presents a two fluid model for simulating free surface compressible flows that handles wave breaking and topological changes implicitly, with flexible equations of state and unconditional hyperbolicity.

Contribution

It introduces an implicit free surface treatment in a two fluid model that can handle complex flow phenomena and variable equations of state.

Findings

Model handles wave breaking naturally

Free surface treated implicitly

Unconditionally hyperbolic for reasonable EOS

Abstract

The purpose of this communication is to discuss the simulation of a free surface compressible flow between two fluids, typically air and water. We use a two fluid model with the same velocity, pressure and temperature for both phases. In such a numerical model, the free surface becomes a thin three dimensional zone. The present method has at least three advantages: (i) the free-surface treatment is completely implicit; (ii) it can naturally handle wave breaking and other topological changes in the flow; (iii) one can easily vary the Equation of States (EOS) of each fluid (in principle, one can even consider tabulated EOS). Moreover, our model is unconditionally hyperbolic for reasonable EOS.