Communications in Mathematical Sciences

Volume 13 (2015)

Number 7

Stable numerical approximation of two-phase flow with a Boussinesq–Scriven surface fluid

Pages: 1829 – 1874

DOI: https://dx.doi.org/10.4310/CMS.2015.v13.n7.a9

Authors

John W. Barrett (Department of Mathematics, Imperial College London, United Kingdom)

Harald Garcke (Fakultät für Mathematik, Universität Regensburg, Germany)

Robert Nürnberg (Department of Mathematics, Imperial College London, United Kingdom)

Abstract

We consider two-phase Navier–Stokes flow with a Boussinesq–Scriven surface fluid. In such a fluid the rheological behavior at the interface includes surface viscosity effects in addition to the classical surface tension effects. We introduce and analyze parametric finite element approximations and show, in particular, stability results for semidiscrete versions of the methods by demonstrating that a free energy inequality also holds on the discrete level. We perform several numerical simulations for various scenarios in two and three dimensions which illustrate the effects of the surface viscosity.

Keywords

incompressible two-phase flow, surface viscosity, Boussinesq–Scriven surface fluid, finite elements, parametric method, stability

2010 Mathematics Subject Classification

35Q35, 65M12, 76D05, 76M10

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Published 19 August 2015