CSD Seminar Series: Konstantin Brenner
The Center for Modeling of Coupled Subsurface Dynamics joins a new 2-year NFR-Aurora collaboration GradFlowPoro (Gradient Flow Modelling of Multi-phase Flow in Deformable Porous Media). Assoc. Prof. Konstantin Brenner, a leading expert in modeling and numerics for multiphase porous media flows in heterogeneous domains, agreed to join our seminar series with a talk.
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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 Assoc. Prof. Konstantin Brenner among the guest speakers.
Short CV: Konstantin Brenner received his PhD from the University Paris-Sud in 2011. In 2012, after a short postdoctoral journey at CEMEF Mines Paristech, he took up his current position as Associate Professor at J.A. Dieudonné laboratory of the University Côte d'Azur, and as a member of the Inria team Coffee.
Contacts: https://math.unice.fr/laboratoire/fiche&id=514
Title of talk: On Richards’ equation and its numerical solution.
Abstract:
Richards’ equation is probably the most popular hydrogeological flow model, which can be used to predict the underground water movement under both saturated and unsaturated conditions. However, despite its importance for hydrogeological applications, Richards' equation has a bad reputation for being difficult to solve numerically. Indeed, depending on the flow parameters, the resolution of the systems arising after the discretization may become a very challenging task, as the linearization schemes such as Picard or Newton’s methods may break down or exhibit unacceptably slow convergence. In this presentation, I will first give a brief overview of Richards’ equation both from the hydrogeological and mathematical perspectives. Then we will discuss the nonlinear preconditioning strategies that can be used to improve the performance of Newton's method. In this regard, I will present some traditional techniques involving the primary variables selection and some recent ones based on the nonlinear Jacobi or block Jacobi preconditioning. The later (block) Jacobi-Newton methods turn out to be a very attractive option as they allow for the convergence analysis in the framework of the Monotone Newton Theorem.
