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Cahn–Hilliard Navier–Stokes Model for the Simulation of Three-Phase Flows The originality of our approach, derived from the Cahn–Hilliard model, comes from the particular form of energy we proposed in Boyer and Lapuerta (M2AN Math Model Numer Anal, 40:653–987,2006), which, among other interesting properties, ensures consistency with the two-phase model
Numerical schemes for a three component Cahn-Hilliard model [26] C Lapuerta, Échanges de masse et de chaleur entre deux phases liquides stratifiées dans un écoulement à bulles Mathématiques appliquées, Université de Provence, France (2006)
Numerical schemes for a threecomponentCahn-Hilliard model F Boyer, C Lapuerta, S Minjeaud and B Piar, A local adaptive refinement method with multigrid preconditioning illustrated by multiphase flows simulations, in CANUM 2008, ESAIM Proc 27, EDP Sciences, Les Ulis (2009) 15–53
A phase-field method for three-phase flows with icing F Boyer, C Lapuerta, S Minjeaud, B Piar, M Quintard, Cahn–Hilliard Navier–Stokes model for the simulation of three-phase flows, Transp Porous Media 82 (2010) 463–483
Cahn–Hilliard Navier–Stokes Model for the Simulation of Three-Phase Flows In order to complete the modelling of three-phase incompressible flows, the Cahn–Hilliard system Boyer et al (2009) is then coupled with Navier–Stokes equations (for more details, see Boyer 2002; Boyer and Lapuerta 2006; Jacqmin 1999; Kim 2005)
Study of a three component Cahn-Hilliard flow model One way to ensure that the values of the concentration c stay between 0 in 1, is to allow degenerate mobility (M(c) = c2(1 c)2 for instance) or non-smooth bulk free energies (e g with logarithmic singularities in 0 and 1)
Scientifc works - math. univ-toulouse. fr C Lapuerta, S Minjeaud, B Piar, M Quintard : Cahn-Hilliard Navier-Stokes model for the simulation of three-phase flows, Transport in Porous Media, Volume 82, Issue 3, pp 463--483 (2010) Published on-line
Cahn-Hilliard Navier-Stokes model for the simulation of three-phase flows The originality of our approach, derived from the Cahn-Hilliard model, comes from the par- ticular form of energy we proposed in Boyer and Lapuerta (M2AN Math Model Numer Anal, 40:653-987,2006), which, among other interesting properties, ensures consistency with the two-phase model