Institut de Mathématiques de Toulouse

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MathOcéan

par Clément Gineste - publié le

Le Groupe de travail MathOcéan a pour but d’impulser des collaborations à l’interface entre les mathématiques et l’océanographie physique (dynamique des géo-fluides, vagues, ondes internes, courants océaniques, etc).
Il est organisé conjointement par des laboratoires bordelais et toulousains. Il s’appuie principalement sur des rencontres bimensuelles alternativement à l’Institut de Mathématique de Bordeaux et à l’Institut Mathématique de Toulouse.




  • Lundi 25 septembre 2017 14:00-15:00 - Jean-François Coulombel - CNRS, Institut de Mathématiques de Toulouse

    La condition aux limites numériques de Neumann pour les équations de transport

  • Lundi 25 septembre 2017 15:00-16:00 - Victor Michel-Dansac - Institut de Mathématiques de Toulouse

    A well-balanced scheme for the shallow-water equations with topography and Manning friction

  • Lundi 27 novembre 2017 14:00-15:00 - Ilya Peshkov - Institut de Mathématiques de Toulouse

    Symmetric hyperbolic formulation for continuum mechanics

    Résumé : We discuss a symmetric hyperbolic framework for modeling
    multiphysics phenomena including momentum, heat, mass, and charge transfer,
    all coupled together. This framework is based on Godunov’s observation about
    the connections between the symmetric hyperbolic conservation laws and
    thermodynamics. The nondissipative part of the time evolution of our
    theory, i.e. which conserves the energy, is represented by symmetric
    hyperbolic equations, while the non-dissipative part, which raises the
    entropy, is represented by algebraic source terms of relaxation type. We
    demonstrate that the classical transport laws such as Newton’s, Fourier’s,
    Fick’s laws which result in the second order parabolic PDEs can be
    successfully modeled within our first order hyperbolic framework. We shall
    discuss some numerical aspects of finding the solution to hyperbolic
    relaxation PDEs. Different numerical examples will be provided justifying
    the proposed approach.


  • Lundi 27 novembre 2017 15:00-16:00 - Gaël Richard - Université de Savoie Mont Blanc

    Consistent equations for open-channel flows

    Résumé : Consistent equations for turbulent open-channel flows on a smooth
    bottom are derived using a turbulence model of mixing length and an
    asymptotic expansion in two layers. A shallow-water scaling is used in an
    upper — or external — layer and a viscous scaling is used in a thin viscous
    — or internal — layer close to the bottom wall. A matching procedure is
    used to connect both expansions in an overlap domain. Depth-averaged
    equations are then obtained in the approximation of weakly-sheared flows
    which is rigorously justified. We show that the Saint-Venant equations with a
    negligible deviation to a flat velocity profile and with a friction law are a
    consistent set of equations at a certain level of approximation. The obtained
    friction law is of the Karman-Prandtl type and successfully
    compared to relevant experiments of the literature. At a higher precision
    level, a consistent three-equation model is obtained with the mathematical
    structure of the Euler equations of compressible fluids with relaxation
    source terms. This new set of equations includes shearing effects and adds
    corrective terms to the Saint-Venant model. At this level of approximation,
    energy and momentum resistances are clearly distinguished. Several
    applications of this new model that pertains to the hydraulics of
    open-channel flows are presented including the computation of backwater
    curves and the numerical resolution of the growing and breaking of roll
    waves.


  • Mercredi 31 janvier 14:00-15:00 - Jan Nordström - Linköping

    Numerical Solution of Initial Boundary Value Problems : Theory and Practise I

    Résumé : Réunion de lancement du projet ANR NABUCO

    Lieu : Salle MIP, bâtiment 1R3


  • Mercredi 31 janvier 15:00-16:00 - David Sanchez - INSA Toulouse, IMT

    A venir

    Résumé : Réunion de lancement du projet ANR NABUCO

    Lieu : Salle MIP, bâtiment 1R3


  • Mercredi 31 janvier 16:30-17:30 - Joackim Bernier - ENS Rennes

    Optimality and resonances in a class of compact finite difference schemes of high order

    Résumé : Réunion de lancement du projet ANR NABUCO

    Lieu : Salle MIP, bâtiment 1R3


  • Jeudi 1er février 09:00-10:00 - Jan Nordström - Linköping

    Numerical Solution of Initial Boundary Value Problems : Theory and Practise II

    Résumé : Réunion de lancement du projet ANR NABUCO

    Lieu : Salle MIP, bâtiment 1R3


  • Jeudi 1er février 10:30-11:30 - Maria Kazakova - IMT

    Modelling shoaling and breaking waves on a mild sloping beach

    Résumé : Réunion de lancement du projet ANR NABUCO

    Lieu : Salle MIP, bâtiment 1R3


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