I’m a Ph.D. student in Mathematics, under the supervision of François Vilar & Fabien Marche at Institut Montpelliérain Alexander Grothendieck (IMAG - UMR 5149).

I’m also a teaching assistant for the Department of Mathematics at Montpellier Faculty of Sciences & Polytech Montpellier Engineering School.

Research interests

During my thesis, I design and implement arbitrary-order methods for partial differential equations arising in the modeling of water waves and wave–structure interactions. For instance, one of the systems I have studied extensively is the nonlinear shallow water equations (NSW), which represent a nonlinear hyperbolic system with source term:

where $\eta$ is water total elevation, $\mathbf{q}=(q_x,q_y)^T$ is the horizontal discharge, and $\mathbf{B} = (0, -g\eta \nabla_{\mathbf{x}} b)^T$ the topography source term. Visitors can find some numerical results and simulation in Softwares.

More generally, I am interested in modeling and numerical analysis of partial differential equations (PDEs), and their applications to physics problems, mainly fluid mechanics.

• Modeling. Conservation laws, non-linear hyperbolic systems, dispersive equations, elliptic equations, models coupling…
• Numerical analysis. Finite elements & discontinuous Galerkin methods, finite volume schemes, monolithic DG-FV subcells & hybrid high-order methods, well-balancing, entropy-preserving schemes, ALE approaches…
• Scientific computing. Object oriented and generic programming, parallel computing…
• Applications. Fluid mechanics, nonlinear shallow water equations, Green-Naghdi equations, wave-structure interactions…

News

• I will participate at the CIMAV 2025 conference in May, held in Aussois, and I am also planning to attend ICOSAHOM 2025 in July, which will take place in Montréal, Canada.
• I started writing my first articles, in collaboration with A. Haidar and my thesis directors, see Research for more details.