Finite Volume approximation of a two-phase two fluxes degenerate Cahn-Hilliard model

05/04/2020
by   Clément Cancès, et al.
0

We study a time implicit Finite Volume scheme for degenerate Cahn-Hilliard model proposed in [W. E and P. Palffy-Muhoray. Phys. Rev. E, 55:R3844-R3846, 1997] and studied mathematically by the authors in [C. Cancès, D. Matthes, and F. Nabet. Arch. Ration. Mech. Anal., 233(2):837-866, 2019]. The scheme is shown to preserve the key properties of the continuous model, namely mass conservation, positivity of the concentrations, the decay of the energy and the control of the entropy dissipation rate. This allows to establish the existence of a solution to the nonlinear algebraic system corresponding to the scheme. Further, we show thanks to compactness arguments that the approximate solution converges towards a weak solution of the continuous problems as the discretization parameters tend to 0. Numerical results illustrate the behavior of the numerical model.

READ FULL TEXT

page 29

page 30

01/30/2020

A convergent entropy diminishing finite volume scheme for a cross-diffusion system

We study a two-point flux approximation finite volume scheme for a cross...
02/26/2020

A corrected decoupled scheme for chemotaxis models

The main purpose of this paper is to present a new corrected decoupled s...
07/18/2019

A variational finite volume scheme for Wasserstein gradient flows

We propose a variational finite volume scheme to approximate the solutio...
12/19/2019

Field model for complex ionic fluids: analytical properties and numerical investigation

In this paper, we consider the field model for complex ionic fluids with...
12/19/2019

Field model for complex ionic fluids

In this paper, we consider the field model for complex ionic fluids with...
06/21/2022

Continuous Data Assimilation for Displacement in a Porous Medium

In this paper we propose the use of a continuous data assimilation algor...
10/29/2018

Novel Near-Optimal Scalar Quantizers with Exponential Decay Rate and Global Convergence

Many modern distributed real-time signal sensing/monitoring systems requ...