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Calcolo
Published in: Calcolo 4/2017

28-07-2017

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

Authors: Elisabetta Repossi, Riccardo Rosso, Marco Verani

Published in: Calcolo | Issue 4/2017

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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.
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Metadata
Title
A phase-field model for liquid–gas mixtures: mathematical modelling and discontinuous Galerkin discretization
Authors
Elisabetta Repossi
Riccardo Rosso
Marco Verani
Publication date
28-07-2017
Publisher
Springer Milan
Published in
Calcolo / Issue 4/2017
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI
https://doi.org/10.1007/s10092-017-0233-4

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