John W. Barrett, Harald Garcke, Robert Nürnberg
Published 2014-04-22Version 1
We consider two-phase Navier--Stokes flow with a Boussinesq--Scriven surface fluid. In such a fluid the rheological behaviour 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 semi-discrete 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.
Comments: 53 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1311.4432
On the Stable Numerical Approximation of Two-Phase Flow with Insoluble Surfactant
Time integration for diffuse interface models for two-phase flow
Two-phase flow with mass density contrast: stable schemes for a thermodynamic consistent and frame-indifferent diffuse-interface model
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