We present a parametric finite element approximation of two-phase flow with insoluble surfactant. This free boundary problem is given by the Navier–Stokes equations for the two-phase flow in the bulk, which are coupled to the transport equation for the insoluble surfactant on the interface that separates the two phases. We combine the evolving surface finite element method with an approach previously introduced by the authors for two-phase Navier–Stokes flow, which maintains good mesh properties. The derived finite element approximation of two-phase flow with insoluble surfactant can be shown to be stable. Several numerical simulations demonstrate the practicality of our numerical method.
DOI : 10.1051/m2an/2014039
Mots clés : Incompressible two-phase flow, insoluble surfactants, finite elements, front tracking, ALE ESFEM
@article{M2AN_2015__49_2_421_0,
author = {Barrett, John W. and Garcke, Harald and N\"urnberg, Robert},
title = {On the stable numerical approximation of two-phase flow with insoluble surfactant},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {421--458},
publisher = {EDP-Sciences},
volume = {49},
number = {2},
year = {2015},
doi = {10.1051/m2an/2014039},
zbl = {1315.35156},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2014039/}
}
TY - JOUR AU - Barrett, John W. AU - Garcke, Harald AU - Nürnberg, Robert TI - On the stable numerical approximation of two-phase flow with insoluble surfactant JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 421 EP - 458 VL - 49 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014039/ DO - 10.1051/m2an/2014039 LA - en ID - M2AN_2015__49_2_421_0 ER -
%0 Journal Article %A Barrett, John W. %A Garcke, Harald %A Nürnberg, Robert %T On the stable numerical approximation of two-phase flow with insoluble surfactant %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 421-458 %V 49 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014039/ %R 10.1051/m2an/2014039 %G en %F M2AN_2015__49_2_421_0
Barrett, John W.; Garcke, Harald; Nürnberg, Robert. On the stable numerical approximation of two-phase flow with insoluble surfactant. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 2, pp. 421-458. doi : 10.1051/m2an/2014039. http://www.numdam.org/articles/10.1051/m2an/2014039/
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