CSD Seminar Series: Clément Cancès

The CSD joins forces with Inria in a 2-year collaboration, funded by the Aurora Mobility Program. Our goal is to develop a thermodynamically consistent mathematical model with a gradient flow structure for multi-phase poromechanics, together with partners from Team RAPSODI from Centre Inria Lille – Nord Europe and the University of Nice. Starting on Monday, the 2nd of May, colleagues from Inria will be visiting us and we will kick-start the collaboration. The center welcomes Dr. Clément Cancès among the guest speakers.

Short CV:  Clément Cancès defended his PhD on in Marseille in 2008, then he served from 2009 to 2015 as a tenured assistant professor (Maître de Conférence) in Paris. He joined Inria and moved to Lille in 2015, where he became a research scientist, then a senior researcher in 2021. His research mainly focuses on mathematical and numerical analysis on models for multicomponent flows, with a particular emphasis on porous media flows.

Contacts: http://chercheurs.lille.inria.fr/ccances/

Title of talk: On a nonlocal Cahn-Hilliard model for incompressible two-phase flows.

Abstract:  We are interested in a phase-field model for a two-phase immiscible and incompressible fluid. The volume of each phase is conserved, and the velocities are prescribed by Darcy's law. In opposition to the classical Cahn-Hilliard equation with degenerate mobility, we do not assume here that the volume fluxes of both phases annihilate, but only that the sum of the volume fluxes is divergence free (which is an Ockham's razor approach to the incompressibility constraint). The resulting system can be interpreted as the Wasserstein gradient flow of a singular energy incorporating the incompressibility constraint. Building on this gradient flow structure, we show the existence of a global weak solution. Numerical simulation illustrate the behavior of the model.

This work has been done in collaboration with Daniel Matthes (TU München, Germany) and Flore Nabet (École Polytechnique, France).