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

M. Shokrpour Roudbari, G. Şimşek, E.H. van Brummelen, K.G. van der Zee

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

42 Citaten (Scopus)


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.

Originele taal-2Engels
Pagina's (van-tot)733-770
Aantal pagina's38
TijdschriftMathematical Models and Methods in Applied Sciences
Nummer van het tijdschrift4
StatusGepubliceerd - 1 apr. 2018


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