To model a liquid–gas mixture, in this article we propose a phase-field approach 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 in 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.

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

Repossi, Elisabetta;Verani, Marco
2017-01-01

Abstract

To model a liquid–gas mixture, in this article we propose a phase-field approach 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 in 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.
2017
Discontinuous Galerkin; Energy-based numerical methods; Liquid–gas mixtures; Metal foams; Modified midpoint; Navier–Stokes–Cahn–Hilliard; Phase-field; Algebra and Number Theory; Computational Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1039131
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