Diffuse-interface two-phase flow models with different densities: a new quasi-incompressible form and a linear energy-stable method

Roudbari, M. Shokrpour and Şimşek, G. and Brummelen, E.H. van and van der Zee, Kristoffer George (2018) Diffuse-interface two-phase flow models with different densities: a new quasi-incompressible form and a linear energy-stable method. Mathematical Models and Methods in Applied Sciences, 28 (4). ISSN 1793-6314

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Abstract

While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this paper, we derive a new form of thermodynamically-consistent quasi-incompressible diffuse-interface Navier–Stokes–Cahn–Hilliard model for a two-phase flow of incompressible fluids with different densities. The derivation is based on mixture theory by invoking the second law of thermodynamics and Coleman–Noll procedure. We also demonstrate that our model and some of the existing models are equivalent and we provide a unification between them. In addition, we develop a linear and energy-stable time-integration scheme for the derived model. Such a linearly-implicit scheme is nontrivial, because it has to suitably deal with all nonlinear terms, in particular those involving the density. Our proposed scheme is the first linear method for quasi-incompressible two-phase flows with non-solenoidal velocity that satisfies discrete energy dissipation independent of the time-step size, provided that the mixture density remains positive. The scheme also preserves mass. Numerical experiments verify the suitability of the scheme for two-phase flow applications with high density ratios using large time steps by considering the coalescence and breakup dynamics of droplets including pinching due to gravity.

Item Type: Article
Additional Information: Electronic version of an article published as Mathematical Models and Methods in Applied Sciences [Volume, Issue, Year, Pages] doi:10.1142/S0218202518500197 ©copyright World Scientific Publishing Company https://www.worldscientific.com/doi/abs/10.1142/S0218202518500197
Keywords: Navier-Stokes Cahn-Hilliard; Quasi-incompressible two-phase-flow; Mixture theory; Thermodynamic consistency; Diffuse interface; Energy-stable scheme
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1142/S0218202518500197
Depositing User: Eprints, Support
Date Deposited: 11 Dec 2017 14:00
Last Modified: 09 May 2018 12:47
URI: http://eprints.nottingham.ac.uk/id/eprint/48655

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