A diffuse interface fractional time-stepping technique for incompressible two-phase flows with moving contact lines
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 3, p. 743-769

For a two phase incompressible flow we consider a diffuse interface model aimed at addressing the movement of three-phase (fluid-fluid-solid) contact lines. The model consists of the Cahn Hilliard Navier Stokes system with a variant of the Navier slip boundary conditions. We show that this model possesses a natural energy law. For this system, a new numerical technique based on operator splitting and fractional time-stepping is proposed. The method is shown to be unconditionally stable. We present several numerical illustrations of this scheme.

DOI : https://doi.org/10.1051/m2an/2012047
Classification:  35Q30,  76D27,  76T99,  65N12
Keywords: Navier Stokes, Cahn Hilliard, multiphase flow, contact line, fractional time-stepping
@article{M2AN_2013__47_3_743_0,
     author = {Salgado, Abner J.},
     title = {A diffuse interface fractional time-stepping technique for incompressible two-phase flows with moving contact lines},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {47},
     number = {3},
     year = {2013},
     pages = {743-769},
     doi = {10.1051/m2an/2012047},
     mrnumber = {3056407},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2013__47_3_743_0}
}
Salgado, Abner J. A diffuse interface fractional time-stepping technique for incompressible two-phase flows with moving contact lines. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 47 (2013) no. 3, pp. 743-769. doi : 10.1051/m2an/2012047. http://www.numdam.org/item/M2AN_2013__47_3_743_0/

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