A diffuse interface fractional time-stepping technique for incompressible two-phase flows with moving contact lines
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 47 (2013) no. 3, pp. 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 : 10.1051/m2an/2012047
Classification : 35Q30, 76D27, 76T99, 65N12
Mots-clés : Navier Stokes, Cahn Hilliard, multiphase flow, contact line, fractional time-stepping 
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     title = {A diffuse interface fractional time-stepping technique for incompressible two-phase flows with moving contact lines},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {743--769},
     publisher = {EDP-Sciences},
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     url = {http://www.numdam.org/articles/10.1051/m2an/2012047/}
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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 , Tome 47 (2013) no. 3, pp. 743-769. doi : 10.1051/m2an/2012047. http://www.numdam.org/articles/10.1051/m2an/2012047/

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