Simulation of Free Surface Compressible Flows Via a Two Fluid Model
  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. 
Frederic Dias (1), Denys Dutykh (1), Jean-Michel Ghidaglia (1) ((1)   CMLA, ENS de Cachan)