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 interdisciplinary project is cosupervised by David Lannes and Philippe Bonneton. It was supported by an IMPT funding until November 2023, and is now funded by the ANR Bourgeons grant.
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 with free surface and varying bathymetry. In particular I am interested in the following topics, all related to a depth-averaged model:
- In the Boussinesq regime:
- Reformulation of the Boussinesq-Abbott model with nonlocal flux and dispersive boundary layer;
- First and second order schemes with efficient treatment of boundary conditions;
- Bathymetry impact on the formation of extreme waves;
- In the nonlinear shallow water regime:
- Asymptotic preserving implicit-explicit schemes for the low Froude limit;
- Fully implicit and iterative kinetic schemes admitting a discrete entropy inequality;
You can contact me at mathieu.rigal[AT]math.u-bordeaux.fr
Education
2019-2022
Ph.D. degree in applied mathematics, Sorbonne University
2016-2019
Engineering degree in applied mathematics and scientific computing
(equivalent to a Master degree), Sup Galilée
2018-2019
Exchange semester at the Technical University of Munich
Publications
Submitted
- General boundary conditions for a Boussinesq model with varying bathymetry [arXiv, HAL]
D. Lannes, R. - Implicit kinetic schemes for the Saint-Venant system [HAL]
C. El Hassanieh, R., J. Sainte-Marie
Proceeding
-
Adaptive wavelet schemes and finite volumes
Daniele Del Sarto, Erwan Deriaz, Xavier Lhebrard, R.
ESAIM: ProcS 70 107-123 (2021)
Thesis manuscript
Talks and presentations
Ile de Ré, May 31, 2024
General boundary conditions for the Boussinesq-Abbott model with varying bathymetry
CANUM 2024
Bordeaux, March 21, 2024
General boundary conditions for the Boussinesq-Abbott model with varying bathymetry
CSM seminar
Slides
Rennes, February 08, 2024
General boundary conditions for a Boussinesq model with varying bathymetry
IRMAR seminar
Bordeaux, February 05, 2024
General boundary conditions for a Boussinesq model with varying bathymetry
GT non permanents, Insitutut de Mathématiques de Bordeaux
Paris, January 12, 2024
Boundary conditions for the Boussinesq-Abbott model
Team ANGE seminar, Inria Paris and LJLL
Paris, January 8, 2024
Boundary conditions for the Boussinesq-Abbott model
Launch of the ANR Bourgeons, LJLL
Amiens, November 17, 2023
Implicit kinetic schemes for the shallow water system
GDR MathGeoPhy
Slides
Bordeaux, November 14, 2023
Implicit kinetic schemes for the shallow water system
Workshop "Analysis, modeling and numerical methods for kinetic models"
Ile d'Aix, October 4, 2023
Boundary conditions for Boussinesq-type models in elevation-flux form
JMVPR workshop
Slides
Bordeaux, June 29, 2023
Implicit kinetic schemes for the Saint-Venant system
NumHyp23 conference
Slides
Bordeaux, June 13, 2023
Implicit kinetic schemes for the Saint-Venant system
Seminar of the team EDP et Physique mathématique at IMB
Slides
Amiens, October 10, 2022
Low Froude regime and implicit kinetic schemes for the Saint-Venant system
Seminar of the LAMFA laboratory, Université de Picardie
Slides
Évian-les-Bains, June 15, 2022
Fully implicit kinetic scheme for the 1D Saint-Venant system
Congrès national d’Analyse NUMérique (CANUM)
Slides
Pornichet, March 10, 2022
Schémas bas Froude IMEX pour les équations de Saint-Venant
Pornichet, MoHyCon conference
Poster
Paris, December 2, 2021
Designing accurate and efficient schemes for the low Froude regime
Inria Paris, team ANGE seminar
Slides
Strasbourg, November 9, 2021
Preserving nearly incompressible states at low Froude number
University of Strasbourg, seminar
Slides
Online, November 16, 2020
Kinetic schemes and wave splitting for the shallow water system in low Froude regime
MathInnov day
Slides
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
Slides
Paris, November 18, 2019
Schéma de reconstruction exact sur les chocs isolés
Inria Paris, team ANGE seminar
Slides
Teaching (fr)
- TD et TP Python d'introduction à l'analyse numérique, niveau L2 (2023) ;
- TD d'analyse hilbertienne, intégration et topologie, niveau L3 (2019-2021) ;
- Cours et révisions d'analyse vectorielle, niveau L2 (2020) ;
- TD d'analyse vectorielle, niveau L2 (2019-2020) ;
- TP d'introduction à Matlab, niveau L1 (2019-2021) ;
Code
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.