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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...
We study a one-dimensional model for two-phase flows in heterogeneous media, in which the capillary pressure functions can
be discontinuous with respect to space. We first give a model, leading to a system of degenerated nonlinear parabolic equations spatially coupled by nonlinear transmission conditions.
We approximate the solution of our problem thanks to a monotonous finite volume scheme. The convergence of the underlying discrete solution
to a weak solution when the discretization step...
In this article, we investigate numerical schemes for solving a three component Cahn-Hilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. Concerning the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the free energy and thus the stability of the method. We study three different schemes and prove existence and convergence theorems. Theoretical results are illustrated by...
In this article, we investigate numerical schemes for solving
a three component Cahn-Hilliard model. The space discretization is
performed by using
a Galerkin formulation and the finite element method.
Concerning the time discretization,
the main difficulty is to write a scheme ensuring,
at the discrete level, the decrease of the free energy
and thus the stability of the method.
We study three different schemes and prove
existence and convergence theorems. Theoretical results are
illustrated by...
In this paper, we propose a new diffuse interface model for the study of three immiscible component incompressible viscous flows. The model is based on the Cahn-Hilliard free energy approach. The originality of our study lies in particular in the choice of the bulk free energy. We show that one must take care of this choice in order for the model to give physically relevant results. More precisely, we give conditions for the model to be well-posed and to satisfy algebraically and dynamically consistency...
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