Simon Clément

Grid Perturbation to simulate location uncertainty

My current research is a collaboration with Etienne Mémin (Inria Rennes), Long Li (Inria Rennes), Jean-Michel Brankart (IGE), Pierre Brasseur (IGE), and AIRSEA team members Eric Blayo and Laurent Debreu. The goal is to understand how a rapidly moving grid can simulate the equations of a fluid under Location Uncertainty. The latter is a framework where stochastic PDEs are used to parameterize the unresolved turbulent motions in a fluid.

Physics-informed discretization of the surface layer

Following the work of my PhD thesis, Sergio Murillo Garcia will work under the joint supervision of Eric Blayo, Florian Lemarié and myself on a new discretization of the atmospheric surface layer. Some modern Finite Volume and Finite Element methods rely on the sub-grid reconstruction of the solution.

We propose to choose a specific logarithmic reconstruction to match the physical theory of the atmospheric surface layer.

PhD: Numerical analysis for a combined space-time discretization of air-sea fluxes and their parameterization

My PhD (defended in November 2022, supervised by Eric Blayo and Florian Lemarié) focused on the air-sea fluxes in numerical models. In a climate model, the exchange of information between ocean and atmosphere is equivalent to a single step of a Schwarz domain decomposition method. I investigated the convergence speed of Schwarz methods for several simplified air-sea models and derived a new discretization based on the physical assumptions of the surface layer.

Publications

• Clement, S., Lemarié, F., Blayo, E. (2024). Semi-discrete analysis of a simplified air-sea coupling problem with nonlinear coupling conditions. In: Dostál, Z., Kozubek, T., Klawonn, A., Langer, U., Pavarino, L.F., Šístek, J., Widlund, O.B. (eds) Domain Decomposition Methods in Science and Engineering XXVII. Lecture Notes in Computational Science and Engineering, vol 149. Springer, Cham. (hal link)
• Clément, S., Lemarié, F., Blayo, E. (2023). Towards a Finite Volume Discretization of the Atmospheric Surface Layer Consistent with Physical Theory. In: Franck, E., Fuhrmann, J., Michel-Dansac, V., Navoret, L. (eds) Finite Volumes for Complex Applications X—Volume 1, Elliptic and Parabolic Problems. FVCA 2023. Springer Proceedings in Mathematics & Statistics, vol 432. Springer, Cham. https://doi.org/10.1007/978-3-031-40864-9_20 (hal link)
• Clement, S., Lemarié, F., Blayo, E. (2022). Discrete Analysis of Schwarz Waveform Relaxation for a Simplified Air-Sea Coupling Problem with Nonlinear Transmission Conditions. In: Brenner, S.C., Chung, E., Klawonn, A., Kwok, F., Xu, J., Zou, J. (eds) Domain Decomposition Methods in Science and Engineering XXVI. Lecture Notes in Computational Science and Engineering, vol 145. Springer, Cham. https://doi.org/10.1007/978-3-030-95025-5_19 (hal link)
• Clement, S., Lemarié, F., Blayo, E. (2022). Discrete analysis of Schwarz waveform relaxation for a diffusion reaction problem with discontinuous coefficients. The SMAI Journal of computational mathematics, Volume 8 (2022), pp. 99-124. doi : 10.5802/smai-jcm.81. (open access)

Teaching

• MAT104 Courses/Tutorial (2019-2021): Mathematical tools for Physics. DLST, 1st year
• Exercises Workshops (2017): Mathematics exercices workshops. La prépa des INP, 1st year

Education

• PhD in Numerical Analysis, UGA, 2019-2022
• Master of Science, Industrial and Applied Mathematics, UGA, 2018-2019
• Engineering school, Applied Mathematics and Computer Science, ENSIMAG, 2016-2019

Contact

firstname.lastname [at] inria [dot] fr

Office 176
Laboratoire Jean Kuntzmann
Bâtiment IMAG
150 Place du Torrent
38401 Saint Martin d’Hères France