Finite volume approximation of a degenerate immiscible two-phase flow model of cahn–hilliard type

Abstract

We propose a two-point flux approximation Finite Volume scheme for a model of incompressible and immiscible two-phase flow of Cahn–Hilliard type with degenerate mobility. This model was derived from a variational principle and can be interpreted as the Wasserstein gradient flow of the free energy. The fundamental properties of the continuous model, namely the positivity of the concentrations, the decay of the free energy, and the boundedness of the Boltzmann entropy, are preserved by the numerical scheme. Numerical simulations are provided to illustrate the behavior of the model and of the numerical scheme.