Research
My fields of specialization and research interests include non linear analysis of Partial Differential Equations,
Numerical Analysis and Computer Simulation. More precisely, I'm interested in the model reduction, the analysis, the construction of Finite
Volume methods and the (multi-dimensional) numerical simulation of
hyperbolic problems arising in fluid mechanics, especially for shallow water flows. A typical example is the
well-known Saint-Venant equations which has a wide range of applications in real life problems.
I advise or advised the PhD of
• Mohammed Ali Debyaoui (Nov. 2016 – 11 Dec. 2020), Applied Mathematics, "Contribution à la modélisation mathématique et numérique pour des modèles d'écoulement non-linéaires dispersifs en eaux peu profondes"
• Jean-Baptiste Clément (Nov. 2017 – 11 Jan. 2021), Fluids Mechanics, "Numerical simulation of flows in unsaturated porous media by an adaptive discontinuous Galerkin method: application to sandy beaches"
• Camille Poussel (Oct. 2021– ), Fluids Mechanics, "Modeling and numerical simulation of flow dynamics in sandy beaches"
• Yolhan Mannes (Oct. 2021– ), Applied Mathematics, "Derivation, mathematical and numerical analysis of models for the cardiovascular system"
• Alioune Ba (Mar. 2023– ), Applied Mathematics, "Mathematical and numerical modeling of sediment transport"
• Mamadou Korca Ba (Mar. 2023– ), Applied Mathematics, "Mathematical and numerical modeling of atmosphere dynamics"
• You can find the list of my publications herein or on Arxiv, Mathscinet, Zentralblatt or HAL
• You can also find my Math Genealogy 
and the
PDF file.
Modeling
Compressible and incompressible flows for shallow water flows, etc
Analysis
Well-posedness, asymptotic behavior, model reduction, etc
Numerical analysis
Finite volume scheme, high order scheme, well-balanced scheme, etc
Numerical simulation (CFD)
AMR, Mesh refinement criterion, Mesh refinement threshold, parallelization, etc
