Mathieu Rigal

Welcome to my personal page!

Since December 2022 I am a post-doctoral researcher in applied mathematics, member of the team EDP et Physique mathématique at Institut de Mathématiques de Bordeaux. This research project is funded by the CNRS.

Between October 2019 and November 2022, I was a Ph.D. candidate at Sorbonne University in the Jacques-Louis Lions laboratory. This work was supervised by Nina Aguillon and Nathalie Ayi, and was funded by the DIM MathInnov. You can find the manuscript of the thesis on the HAL portal.

My research focuses on the design, study and implementation of efficient numerical schemes for simulating complex geophysical flows. In particular I am interested in the following topics:

You can contact me at mathieu.rigal[AT]


Ph.D. degree in applied mathematics, Sorbonne University

Engineering degree in applied mathematics and scientific computing (equivalent to a Master degree), Sup Galilée

Exchange semester at the Technical University of Munich



Proceeding CEMRACS 2019

Thesis manuscript

Talks and presentations

Amiens, October 10, 2022
Low Froude regime and implicit kinetic schemes for the Saint-Venant system
Seminar of the LAMFA laboratory, Université de Picardie

Évian-les-Bains, June 15, 2022
Fully implicit kinetic scheme for the 1D Saint-Venant system
Congrès national d’Analyse NUMérique (CANUM)

Pornichet, March 10, 2022
Schémas bas Froude IMEX pour les équations de Saint-Venant
Pornichet, MoHyCon conference

Paris, December 2, 2021
Designing accurate and efficient schemes for the low Froude regime
Inria Paris, team ANGE seminar

Strasbourg, November 9, 2021
Preserving nearly incompressible states at low Froude number
University of Strasbourg, seminar

Online, November 16, 2020
Kinetic schemes and wave splitting for the shallow water system in low Froude regime
MathInnov day

Online, June 16, 2020
Schémas cinétiques et splitting d'ondes pour les équations de Saint-Venant en régime bas Froude
Inria Paris, team ANGE seminar

Paris, November 18, 2019
Schéma de reconstruction exact sur les chocs isolés
Inria Paris, team ANGE seminar

Teaching (fr)


The program swimpy-1d provides solvers for the one dimensionnal shallow water system in a Python framework. It features explicit and implicit kinetic solvers alongside hydrostatic reconstruction for preserving the lakes at rest and the positivity.