Sacha Cardonna

Sacha Cardonna

Ph.D. Student in Mathematics

Hello there! ☺

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:

$$ \begin{cases} \partial_t\:\!\eta + \nabla_{\!\mathbf{x}} \cdot \mathbf{q} = \mathbf{S}_1[b](\mathbf{v}), \\ \partial_t \:\!\mathbf{q} + \nabla_{\!\mathbf{x}} \cdot \left( \mathbf{u} \otimes \mathbf{q} + \frac{g\eta}{2}(\eta - 2b)\mathbb{I}_2 \right) = \mathbf{S}_2[b](\mathbf{v}), \end{cases} \nonumber $$

with $\mathbf{v} = (\eta,\mathbf{q})^t$, where $\eta$ is water total elevation, $\mathbf{q}$ is the horizontal discharge, and $\mathbf{S}[b](\mathbf{v})$ is a generic source term that may contains topography, friction and/or Coriolis effects. 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 & highlights

  • I talked about my thesis work at ICOSAHOM 2025 in Montréal, see the slides.
  • During MIPS Week, I talked about some aspects of modeling and scientific computing to non-experts scientists, see the presentation.
  • Recently made a presentation at the CIMAV 2025 conference in May, held in Aussois, see the beamer.
  • Started writing my first articles, in collaboration with A. Haidar and my thesis directors, see Research for more details.