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Séminaire Equations aux dérivées partielles

organisé par l'équipe Modélisation et contrôle

  • Marie Boussard

    Estimation of numerical entropy loss via a projection method

    3 mars 2026 - 14:00Salle de conférences IRMA

    Ocean circulation models cover a spatial domain up to the planetary scale. Due to computational constraints, numerical simulations therefore rely on relatively coarse meshes, with cell areas of the order of 10 000 km^2. As a consequence, finite volume schemes used for discretization induce a significant numerical entropy loss. This phenomenon leads to unphysical behaviours in the simulation result, such as the mixing of water masses with distinct temperatures and salinities. To address this problem, referred to as "spurious mixing" by oceanographers, localizing and quantifying this numerical entropy loss in high-order codes is crucial. A method was proposed by Aguillon, Audusse, Desveaux and Salomon, but is limited to the one-dimensional case.

    I will introduce a method suitable for simulations in two dimensions of space, including high order schemes and in the presence of source terms. This approach relies on projecting a consistent flux onto the set of fluxes satisfying a discrete entropy inequality. The projection is carried out by an optimization algorithm with inequality constraints. Then, I will discuss the theoretical guarantees provided by the method, in particular the establishment of a Lax-Wendroff-type theorem, and conclude with numerical results for the shallow water equations.

    This is a joint work with Nina Aguillon and Julien Salomon.

  • Guillaume De Romémont

    A data-driven learned discretization approach for Finite Volume schemes

    10 mars 2026 - 14:00Salle de conférences IRMA

    The recent development of Machine Learning (ML) and Deep Learning methods, coupled with recent advances in GPU-based computing defined new promising techniques for the numerical resolution of PDEs entirely solved with ML, as well as tuning existing algorithms for learning corrections or discretizations. In this work, we combine finite volume numerical schemes and neural networks to learn the discretization of the spatial derivatives of partial differential equations (PDEs) in order to better resolve the small spatial scales. We use approximate solutions of the 1D and 2D Euler equations obtained on a finer grid for the reference database in order to learn an optimal spatial discretization on a coarse grid, even with discontinuities in the solution. We post-process the outputs of the neural network to propose an interpretable, entropy consistent subgrid-model with super-resolution capabilities within a second-order finite volume solver without violating physical constraints.

  • Corentin Gentil

    A linear model of ocean western boundary currents with bathymetry and topography

    17 mars 2026 - 14:00Salle de conférences IRMA

    The trajectory of ocean western boundary currents is crucial in climate simulations, but the contribution of each physical effect to its path, like wind forcing, stratification, rotation, inertia, geometry of the coast, etc. remains an open question. In this presentation, I will introduce a simplified model for oceanic motion close to the Boussinesq equations, which takes into account two effects that are essential for predicting the trajectory of ocean western boundary currents: stratification and topography. We will see how to construct an approximate solution to this system as a superposition of interior terms on the one hand, and boundary layer terms of different natures on the other hand, due to small parameters. We will study how topography and stratification affect the solution and discuss different asymptotics created by small and large parameters.

  • Mabrouk Ben Jaba

    TBA

    24 mars 2026 - 14:00Salle 301

  • Takéo Takahashi

    TBA

    31 mars 2026 - 14:00Salle de conférences IRMA

    TBA

  • Tiphaine Delaunay (a Confirmer)

    TBA

    7 avril 2026 - 14:00Salle de conférences IRMA

    TBA

  • Chloé Mimeau

    TBA

    28 avril 2026 - 14:00Salle de conférences IRMA

  • Aline Lefebvre-Lepot

    TBA

    5 mai 2026 - 14:00Salle de conférences IRMA

    TBA

  • Lukas Renelt

    TBA

    19 mai 2026 - 14:00Salle de conférences IRMA

    TBA