Research

My research interests

Numerical Analysis of PDEs, Scientific Computing, and Computational Fluid Dynamics, with particular emphasis on:

  • Mesh adaptation using the adaptive multi-resolution framework for lattice Boltzmann methods [P2, P3, P4, P5].
  • Numerical analysis (consistency, convergence, stability, and boundary conditions) of lattice Boltzmann methods [P6, P7, P8, P9, C1].
  • Development and analysis of high-order kinetic schemes [P9, P10].
  • Simulation of multiphase flows using the level-set theory on highly adaptive data structures (quadtree and octree meshes) [P1]

Publications on peer-reviewed journals and preprints

  • [P10] Fourth-order entropy-stable lattice Boltzmann schemes for hyperbolic systems
    T. Bellotti, P. Helluy, L. Navoret
    Submitted, 2024 [Preprint HAL]
  • [P9] The influence of parasitic modes on stable lattice Boltzmann schemes and weakly unstable multi-step Finite Difference schemes
    T. Bellotti
    Submitted, 2024 [Preprint HAL]
  • [P8] Initialisation from lattice Boltzmann to multi-step Finite Difference methods: Modified equations and discrete observability
    T. Bellotti
    Journal of Computational Physics, Vol. 504, 112871, 2024 [Preprint HAL, Publication website]
  • [P7] Truncation errors and modified equations for the lattice Boltzmann method via the corresponding Finite Difference schemes
    T. Bellotti
    ESAIM: Mathematical Modelling and Numerical Analysis, 57 (3) 1225--1255, 2023 [Preprint HAL, Publication website]
  • [P6] Finite Difference formulation of any lattice Boltzmann scheme
    T. Bellotti, B. Graille, M. Massot
    Numerische Mathematik, Vol. 152, Pages 1--40, 2022 [Preprint HAL, Preprint arXiv, Publication website]
  • [P5] Does the multiresolution lattice Boltzmann method allow to deal with waves passing through mesh jumps?
    T. Bellotti, L. Gouarin, B. Graille, M. Massot
    Compte Rendus Mathématique, Vol. 360, Pages 761--769, 2022 [Preprint HAL, Preprint arXiv, Publication website]
  • [P4] High accuracy analysis of adaptive multiresolution-based lattice Boltzmann schemes via the equivalent equations
    T. Bellotti, L. Gouarin, B. Graille, M. Massot
    SMAI Journal of Computational Mathematics, Vol. 8, Pages 161--199, 2022 [Preprint HAL, Preprint arXiv]
  • [P3] Multidimensional fully adaptive lattice Boltzmann methods with error control based on multiresolution analysis
    T. Bellotti, L. Gouarin, B. Graille, M. Massot
    Journal of Computational Physics, Vol. 471, 111670, 2022 [Preprint HAL, Preprint arXiv]
  • [P2] Multiresolution-based mesh adaptation and error control for lattice Boltzmann methods with applications to hyperbolic conservation laws
    T. Bellotti, L. Gouarin, B. Graille, M. Massot
    SIAM Journal on Scientific Computing, Vol. 44, Iss. 4, 2022 [Preprint HAL, Preprint arXiv]
  • [P1] A coupled level-set and reference map method for interface representation with applications to two-phase flows simulation
    T. Bellotti, M. Theillard
    Journal of Computational Physics, Vol. 392, Pages 266--290, 2019 [Preprint / Link]

Conference papers

  • [C1] Monotonicity for Genuinely Multi-step Methods: Results and Issues From a Simple Lattice Boltzmann Scheme
    T. Bellotti
    Finite Volumes for Complex Applications X--Volume 2, Hyperbolic and Related Problems, 2023 [Link]

PhD disseration

  • Numerical analysis of lattice Boltzmann schemes : from fundamental issues to efficient and accurate adaptive methods - Link
    Defended on 1st June 2023 at Ecole polytechnique (France).

Editorial activity

Talks

  • March 2024 - Invited at Séminaire d'analyse numérique de l'IRMAR - Rennes (France)
    L'importance d'être stable et schémas cinétiques d'ordre élevé
  • March 2024 - Séminaire Analyse numérique et équations aux dérivées partielles - Lille (France)
    L'importance d'être stable et schémas cinétiques d'ordre élevé
  • February 2024 - Séminaire EDP et Applications - Nancy (France)
    Analyse numérique des schémas de Boltzmann sur réseau : des questions fondamentales aux méthodes adaptatives efficientes et précises
  • February 2024 - Séminaire A3 (équipe Analyse Appliquée) - Amiens (France)
    Analyse numérique des schémas de Boltzmann sur réseau : des questions fondamentales aux méthodes adaptatives efficientes et précises
  • February 2024 - Séminaire EDP, Analyse et Applications - Metz (France)
    Analyse numérique des schémas de Boltzmann sur réseau : des questions fondamentales aux méthodes adaptatives efficientes et précises
  • January 2024 - Invited at Séminaire équipe Calcul scientifique et Modélisation - Bordeaux (France)
    Analyse numérique des schémas de Boltzmann sur réseau : des questions fondamentales aux méthodes adaptatives efficientes et précises
  • January 2024 - Invited at Séminaire équipe INRIA ANGE - Paris (France)
    Numerical analysis of lattice Boltzmann schemes: from fundamental issues to efficient and accurate adaptive methods
  • November 2023 - Invited at Séminaire EDP du LMV - Versailles (France)
    Finite Difference formulation of any lattice Boltzmann scheme: consistency, stability, convergence, and monotonicity
  • October 2023 - Conference ``Finite Volumes for Complex Applications 10 (FVCA10)'' Strasbourg (France)
    Monotonicity for genuinely multi-step methods: results and issues from a simple lattice Boltzmann scheme
  • August 2023 - Conference ``Numerical Analysis in the 21st Century'' - Oxford (UK)
    Finite Difference formulation of any lattice Boltzmann scheme  : consistency, stability and convergence
  • July 2023 - Invited at the 19th International Conference for Mesoscopic Methods in Engineering and Science - Chengdu (China)
    Initialization from lattice Boltzmann to multi-step Finite Difference methods  : modified equations and discrete observability
  • April 2023 - Conference 22th IACM - CFC 2023 - Cannes (France)
    Initialization from lattice Boltzmann to multi-step Finite Difference methods  : modified equations and discrete observability
  • February 2023 - Invited at Groupe de Travail d'EDP et Calcul Scientifique du LMRS et LMI - Rouen (France)
    Finite Difference formulation of any lattice Boltzmann scheme  : consistency and stability (and initialization)
  • December 2022 - Invited at séminaire de l'IRMAR - Rennes (France)
    Finite Difference formulation of any lattice Boltzmann scheme  : consistency and stability
  • November 2022 - Invited at the workshop ``Schémas numériques de type Boltzmann'' - Bordeaux (France)
    Initialisation pour les schémas de Boltzmann sur réseau : aspects discrets et asymptotiques
  • October 2022 - Invited at séminaire EDP - Strasbourg (France)
    Finite Difference formulation of any lattice Boltzmann scheme : consistency and stability
  • September 2022 - Talk at von Karman Institute - Bruxelles (Belgium)
    Lattice Boltzmann schemes on dynamically adapted meshes relying on multiresolution and recent theoretical breakthroughs in the understanding of lattice Boltzmann methods
  • July 2022 - Conference 32nd Internation Symposium on Rarefied Gas Dynamics - Seoul (South Korea)
    Limits of the Kinetic Interpretation of Lattice Boltzmann Schemes : A Cure via a Macroscopic Standpoint with Finite Difference Schemes on the Conserved Moments
  • June 2022 - Conference 18th International Conference for Mesoscopic Methods in Engineering and Science - La Rochelle (France)
    Finite Difference formulation of lattice Boltzmann schemes : consequences on consistency and stability
  • June 2022 - Conference 45ème Congrès d'Analyse Numèrique (CANUM) - Evian-les-Bains (France)
    Consistency and stability of lattice Boltzmann schemes
  • March 2022 - Invited at séminaire Analyse Numérique et EDP - Orsay (France)
    Finite Difference formulation of any lattice Boltzmann scheme
  • January 2022 - Invited at the 34ème séminaire CEA/GAMNI - Paris (France)
    Finite Difference formulation of any lattice Boltzmann scheme
  • November 2021 - Workshop ``Schémas de Boltzmann sur réseau'' - Paris (France)
    Une formulation de type différences finies pour les schémas de Boltzmann sur réseau
  • October 2021 - Invited at the workshop `` Modèles et méthodes pour les équations cinétiques'' - Bordeaux (France)
    Une formulation de type différences finies pour les schémas de Boltzmann sur réseau
  • July 2021 - Conference 17th International Conference for Mesoscopic Methods in Engineering and Science - Online
    Fully adaptive lattice Boltzmann methods based on multiresolution analysis : error control, high accuracy, equivalent equations and grid jumps
  • June 2021 - Conference 10ème Biennale Française des Mathématiques Appliquées - La Grande-Motte (France)
    Fully adaptive lattice Boltzmann methods with error control based on multiresolution analysis
  • May 2021 - Workshop ``Schémas de Boltzmann sur réseau'' - Paris (France)
    Adaptive multiresolution-based lattice Boltzmann schemes and their accuracy analysis via the equivalent equations
  • January 2021 - Conference WCCM ECCOMAS 2020 - Online
    A class of multidimensional fully adaptive lattice-Boltzmann methods based on multiresolution analysis
  • January 2021 - Conference WCCM ECCOMAS 2020 - Online
    A coupled level-set and reference map method for interface representation with applications to two-phase flows simulation

Responsibility and organization

  • 02/06/23 - Responsible for the workshop "Around numerical analysis of lattice Boltzmann methods" - Ecole polytechnique - around 50 participants (half on site, half online) - Website
  • 2022--2023 - Responsible for the team workshop Team HPC@Maths - Ecole polytechnique
  • 10/20--10/21 - Vice-president of the organization committee CJC-MA 2021 Congrès des Jeunes Chercheuses et Chercheurs en Mathématiques Appliquées - Ecole polytechnique - around 100 participants

 

Other works

      • Modellizzazione dell’effetto loto tramite le equazioni di Allen-Cahn e di Cahn-Hilliard, T. Bellotti, BSc Thesis, 2017 [Link, in Italian]

 

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