Keywords : mathematical modeling; 2D-1D model coupling; multi-scale modeling; hyperbolic systems; shallow water equations; asymptotic expansions; scientific computing

My current work focuses on the mathematical modeling and the numerical simulation of rivers and estuaries.

• I first developed a new 1D mathematical model that takes into account the specific shape of a river or an estuary (where the longitudinal dimension is much larger than the transverse dimension).
• Now, I am working on the operational implementation of this model (this is a collaboration with the SHOM). More specifically, coupling an estuary modeled in 1D and an ocean model will yield accurate boundary conditions for the ocean model.
• In addition to this work, I develop new models that take into account the small scale variations of a river topography, assuming that it is given by a main slope to whom a small perturbation is added.

Keywords : Euler equations; low Mach number limit; finite volume schemes; IMplicit-EXplicit time discretizations; asymptotic-preserving schemes; MOOD techniques

My first post-doctoral research position was dedicated to the derivation of a numerical scheme for the compressible Euler equations that is valid for all Mach number regimes. In this setting, the main difficulty stems from the temporal singularity of the low Mach number limit. We worked within the IMEX (IMplicit-EXplicit) framework to increase the time accuracy. A relevant convex combination procedure ensured the stability of this newly derived numerical scheme.

Keywords : shallow water equations; nonlinear friction; moving steady states; hyperbolic systems; finite volume schemes; Godunov-type schemes; well-balanced schemes; very high-order schemes (in space and time); SSPRK time discretization; MOOD techniques; scientific computing; parallel computing

Over the course of my PhD, I mainly studied the numerical approximation of solutions to hyperbolic systems of conservation laws with source terms. This work was supported by the ANR GeoNum grant.

• numerical schemes for conservation laws with source terms, mainly applied to the shallow water equations with topography and friction source terms, and that:
  • preserve the water height positivity
  • allow treatment of transitions between wet and dry areas
  • preserve all the steady states of the shallow water equations with a generic source term (well-balance property)
• high-order schemes and MOOD techniques: application to the shallow water equations, high order of accuracy and preservation of several steady state solutions on a 2D uniform Cartesian grid
• OpenMP parallelization of my 2D Fortran code for large-scale geophysical simulations
• "genuinely multidimensional" schemes for the Euler equations, approximated using a Cartesian grid
• GRP schemes - that approximate solutions to a Generalized Riemann Problem - applied to conservation laws