no. 3
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
Keywords: 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},
     year = {2013},
     publisher = {EDP Sciences},
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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

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