Research

Research interests

• Modelling: degenerate parabolic equation, flow in unsaturated/saturated  porous media, Richards' equation, Darcy's law, anisotropy, heterogeneity, volume averaging method (upscaling), seepage

• Numerical methods: Discontinuous Galerkin methods, BDF methods, adaptive mesh refinement, a posteriori indicators, adaptive time stepping, nonlinear solver with relaxation, weak penalization

• Computation: Hybrid non-conforming unstructured mesh, 2D/3D simulations, block-based meshing tool, parent-child data stucture, multiple space-/time scales, high-order

• Applications: sandy beach, swash groundwater dynamics, wave forcing, coastal engeneering, geophysical flows

My projects

I pursued my PhD thesis (2017 - 2020) at IMATH and MIO laboratories from the University of Toulon (France) under the supervision of Frédéric Golay (IMATH), Mehmet Ersoy (IMATH) and Damien Sous (MIO). The subject was about “Numerical simulation of unsaturated porous media flows by an adaptive discontinuous Galerkin method: application to sandy beaches”. The motivation is to provide a robust, efficient and accurate tool to model and compute wave-induced flows inside sandy beaches. In particular, I focused on Richards' equation to model flow dynamics in unsaturated porous media. Despite its current use, this equation is numerically challenging to solve for a wide range of cases, for instance in presence of steep wetting fronts. Moreover, at the start of my PhD, I decided to use Discontinuous Galerkin (DG) methods because of their flexibility, in particular for adaptive mesh refinement. Based on these choices, I developed a computational code called Rivage which demonstrates its abilities for such simulations through various numerical examples.

I defended my PhD thesis on the 11th Janaury 2021 in front of a jury made up of:

• Philippe Helluy, Professor, University of Strasbourg - President of the Jury

• Vít Dolejší, Professor, Charles University in Prague - Reviewer

• Philippe Ackerer, Professor, University of Strasbourg - Reviewer

• Béatrice Rivière, Professor, Rice University - Examiner

• France Floc'h, Lecturer, University of Western Brittany - Examiner

• Stéphane Bonelli, Research Director, INRAE - Invited

I was in a PostDoc for 2021 at Géosciences Montpellier laboratory from the University of Montpellier (France). I was mentored by Frédéric Bouchette. The aim was to continue my PhD work by carrying extended applications concerning large-scale experiments and real beaches. This should provide new insights and perspectives about the physics for the oceanographic/littoralist community. In addition, I am improving Rivage code for the simulation of Richards' equation by taking care more specifically of the nonlinearities and degeneracies rising at multiple space/time scales.

I am currently involved in a PostDoc at the Department of Technical Mathematics, Faculty of Mechanichal Engineering in the Czech Technical University in Prague. I am mentored by Petr Sváček. The project deals with the development of high order discontinuous Galerkin methods for numerical solution of PDEs in the continuum mechanics.