A phase-field model for liquid-gas mixtures: mathematical modelling and Discontinuous Galerkin discretization

27/2016

A phase-field model for liquid-gas mixtures: mathematical modelling and Discontinuous Galerkin discretization

Monday 25th July 2016

Repossi, E.; Rosso, R.; Verani, M.

In this article we propose a phase-field approach to model a liquid-gas mixture that might also provide a description of the expansion stage of a metal foam inside a hollow mold. We conceive the mixture as a two-phase incompressible-compressible fluid governed by a Navier-Stokes-Cahn-Hilliard system of equations, and we adapt the Lowengrub-Truskinowsky model to take into account the expansion of the gaseous phase. The resulting system of equations is characterized by a velocity field that fails to be divergence-free, by a logarithmic term for the pressure that enters the Gibbs free-energy expression and by the viscosity that degenerates in the gas phase. In the second part of the article we propose an energy-based numerical scheme that, at the discrete level, preserves the mass conservation property and the energy dissipation law of the original system. We use a Discontinuous Galerkin approximation for the spatial approximation and a modified midpoint based scheme for the time approximation.