Welcome to my personal page!

After defending my thesis in November 2022, I have been working as a post-doctoral reasearcher from the team EDP et Physique mathématique at Institut de Mathématiques de Bordeaux (December 2022 -- November 2024), and as a member of the LJLL team at Sorbonne Université (since December 2024). My current research consists in an interdisciplinary project cosupervised by David Lannes and Philippe Bonneton, and was supported by different fundings (IMPT, ANR Bourgeons, ERC BLOC).

Between October 2019 and November 2022, I was a Ph.D. candidate at Sorbonne Université in the LJLL team. This work was supervised by Nina Aguillon, Nathalie Ayi and Jacques Sainte-Marie, 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 (based on PDE analysis), 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

Published and accepted

• C. El Hassanieh, M. Rigal, J. Sainte-Marie. "Implicit kinetic schemes for the Saint-Venant system".
  ESAIM: M2AN (2025) [HAL]
  
  
• D. Lannes and M. Rigal. "General boundary conditions for a Boussinesq model with varying bathymetry".
  In: Studies in Applied Mathematics (2024) [SAPM, arXiv, HAL]
  
  
• D. Del Sarto, E. Deriaz, X. Lhebrard, M. Rigal. "Adaptive wavelet schemes and finite volumes".
  ESAIM: ProcS 70 107-123 (2021) [ESAIM]

Thesis manuscript

• Low Froude regime and implicit kinetic schemes for the Saint-Venant system

Talks and presentations

Conferences and workshops

• Journées jeunes EDPistes 2025, Nice, January 9, 2025
• CANUM 2024, Ile de Ré, May 31, 2024
• GDR MathGeoPhy, Amiens, November 17, 2023
• Workshop "Analysis, modeling and numerical methods for kinetic models", Bordeaux, November 14, 2023
• JMVPR workshop, Ile d'Aix, October 4, 2023
• NumHyp23 conference, Bordeaux, June 29, 2023
• Congrès national d’Analyse NUMérique (CANUM), Évian-les-Bains, June 15, 2022

• Stochastic parameterization half-day, Paris, March 5, 2025
• CSM seminar, Bordeaux, March 21, 2024
• IRMAR seminar, Rennes, February 08, 2024
• GT non permanents, Institut de Mathématiques de Bordeaux, Bordeaux, February 05, 2024
• Team ANGE seminar, Inria Paris and LJLL, Paris, January 12, 2024
• Launch of the ANR Bourgeons, LJLL, Paris, January 8, 2024
• Seminar of the team EDP et Physique mathématique at IMB, Bordeaux, June 13, 2023
• Seminar of the LAMFA laboratory, Université de Picardie, Amiens, October 10, 2022
• Inria Paris, team ANGE seminar, Paris, December 2, 2021
• University of Strasbourg, seminar, Strasbourg, November 9, 2021
• MathInnov day, Online, November 16, 2020
• Inria Paris, team ANGE seminar, Online, June 16, 2020
• Inria Paris, team ANGE seminar, Paris, November 18, 2019

• MoHyCon conference, Pornichet, March 10, 2022

A few slides:

• General boundary conditions for the Boussinesq-Abbott model with varying bathymetry [slides]
• Low Froude IMEX scheme for the Saint-Venant system [poster, slides]
• Implicit kinetic schemes for the Saint-Venant system [slides]
• Schémas cinétiques et splitting d'ondes pour les équations de Saint-Venant [slides]
• Schéma de reconstruction exact sur les chocs isolés [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

BA_waves is a Matlab code allowing to simulate water waves with weakly dispersive effects as described by the Boussinesq-Abbott model. General boundary conditions are treated without the need for a sponge layer or the source function method, but instead involve a nonlocal flux and dispersive boundary layer. It also offers the possibility to deactivate the dispersive effects in part of the computational domain to better describe the breaking of waves with the hyperbolic shallow water system.

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.