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Séminaire Equations aux dérivées partielles

organisé par l'équipe Modélisation et contrôle

  • Finite Difference formulation of any lattice Boltzmann scheme: consistency and stability

    — Thomas Bellotti

    11 octobre 2022 - 14:00Salle de conférences IRMA

    Lattice Boltzmann schemes rely on the enlargement of the size of the target problem in order to solve PDEs in a highly parallelizable and efficient kinetic-like fashion, split into a collision and a stream phase. This structure, despite the well-known advantages from a computational standpoint, is not suitable to construct a rigorous notion of consistency with respect to the target equations and to provide a precise notion of stability. In order to alleviate these shortages and introduce a rigorous framework, we demonstrate that any lattice Boltzmann scheme can be rewritten as a corresponding multi-step Finite Difference scheme on the conserved variables. This is achieved by devising a suitable formalism based on operators, commutative algebra and polynomials. Therefore, the notion of consistency of the corresponding Finite Difference scheme allows to invoke the Lax-Richtmyer theorem in the case of linear lattice Boltzmann schemes. Moreover, we show that the frequently-used von Neumann-like stability analysis for lattice Boltzmann schemes entirely corresponds to the von Neumann stability analysis of their Finite Difference counterpart. More generally, the usual tools for the analysis of Finite Difference schemes are now readily available to study lattice Boltzmann schemes. Their relevance is verified by means of numerical illustrations.

  • TBA

    — Léopold Trémant

    18 octobre 2022 - 14:00Salle de conférences IRMA

  • Preserving discrete involutions on Cartesian grids

    — Wasilij Barsukow

    15 novembre 2022 - 14:00Salle de conférences IRMA

  • TBA

    — Virginie Ehrlacher

    22 novembre 2022 - 14:00Salle de conférences IRMA

  • TBA

    — Geshkovski Borjan

    29 novembre 2022 - 14:00Salle de conférences IRMA

  • TBA

    — Amina Mecherbet

    10 janvier 2023 - 14:00A confirmer

  • TBA

    — Eloi Martinet

    24 janvier 2023 - 14:00Salle de conférences IRMA

  • TBA

    — Andrea Thomann

    7 février 2023 - 14:00A confirmer

  • Analysis of the Shallow Water equations with two velocities

    — Nelly Boulos Al Makary

    14 mars 2023 - 14:00Salle de conférences IRMA