Geodesic
On the stable numerical approximation of two-phase flow with insoluble surfactant
Barrett, John W.1 ; Garcke, Harald2  ; Nürnberg, Robert1
1 Department of Mathematics, Imperial College, London, SW7 2AZ, UK.
2 Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 2, pp. 421-458

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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.

Reçu le :
DOI : 10.1051/m2an/2014039
Classification : 35Q35, 65M12, 76D05, 76D27, 76M10
Keywords: Incompressible two-phase flow, insoluble surfactants, finite elements, front tracking, ALE ESFEM

Barrett, John W. 1 ; Garcke, Harald 2 ; Nürnberg, Robert 1

1 Department of Mathematics, Imperial College, London, SW7 2AZ, UK.
2 Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany. 
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     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},
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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

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