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Finite volume approximation of a degenerate immiscible two-phase flow model of {C}ahn-{H}illiard 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.
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https://hal.archives-ouvertes.fr/hal-01468795
Contributor : Clément Cancès Connect in order to contact the contributor
Submitted on : Wednesday, February 15, 2017 - 5:26:55 PM
Last modification on : Friday, November 26, 2021 - 8:38:07 AM
Long-term archiving on: : Tuesday, May 16, 2017 - 3:24:41 PM

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Clément Cancès, Flore Nabet. Finite volume approximation of a degenerate immiscible two-phase flow model of {C}ahn-{H}illiard type. FVCA8 2017 - International Conference on Finite Volumes for Complex Applications VIII, 2017, Lille, France. pp.431-438. ⟨hal-01468795⟩

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