A Five-Equation Model for the Simulation of Interfaces between Compressible Fluids

A diffuse-interface method is proposed for the simulation of interfaces between compressible fluids with general equations of state, including tabulated laws. The interface is allowed to diffuse on a small number of computational cells and a mixture model is given for this transition region. We write conservation equations for the mass of each fluid and for the total momentum and energy of the mixture and an advection equation for the volume fraction of one of the two fluids. The model needs an additional closure law. We study two different closure laws: isobaric and isothermal. We study the mathematical properties of the resulting models: consistency, hyperbolicity, and existence of a mathematical entropy. We also study the stability of the interfaces with respect to averaging due to the numerical diffusion, a crucial property for the simulation of interface problems by conservative schemes. We show that the isobaric closure is preferable to the isothermal closure with respect to this property. We propose a Roe-type numerical scheme for the simulation of the model and show numerical results for classical test cases.