Research themes


My objective is to develop and enhance tools to use for industrial problems. These tools can be numerical schemes, methods, or procedures. The most important activities are summarized hereafter.

Finite Volume discretization

Even if the Finite Volume method is developed for more than 20 years and is routinely applied in the industry, it still has some flaws. Indeed, the FV method is well known in the context of structured grids but its use for unstructured grids still presents defaults and needs additional effort. Switching to unstructured grids is an industrial prerequisite.
There are today two main approaches for unstructured grids:
  • the cell-centered finite volume method considers the mesh elements as control volumes. People generally consider multi-element shape meshes and even polyhedra. This approach is generally preferred in the industry since it is the natural extension of the standard structured approach. It enables the recovery of standard practice for mesh generation to capture the boundary layer, where solution and gradients must be captured accurately.
  • using a dedicated method, the node-centred finite volume method builds the control volume around mesh nodes. The control volume is then called a dual cell. The main advantage of the procedure lies in mesh adaptation. Indeed, the association between dual-cell and mesh-node enables us to compute mesh adaptation sensor "at mesh node".
I am working on the cell-centered formulation for the definition of gradient and successive derivatives, trying to avoid the least square formulation over an extended stencil due to its bad condition number. The schemes are mandatory for the MUSCL reconstruction or for the diffusion terms. My research on the node-centred formulation focuses on the extension of the schemes to multi-physics, including multi-species reacting flows, aerothermodynamics, and plasmas. Of course, the goal is to apply the node-centred method to mesh adaptation.

Cooperation: G. Barreau (ONERA/DPHY), F. Pechereau (ONERA/DPHY), F. Tholin (ONERA/DPHY), J. Vanharen (Inria), B. Maugars (DAAA/CLEF), C. Content (DAAA/CLEF), A. Loseille (INRIA/Gamma), F. Alauzet (INRIA/Gamma), D. Zuzio (DMPE/MH), J-L. Estiveleses (DMPE/MH), and engineers at Safran Tech.

Mesh adaptation for multi-physics

The mesh adaptation procedure for steady flows consists of the convergence of the couple mesh and solution using one’s favorite solver equipped with dedicated schemes. The proof of the procedure/concept follows more than twenty years of research in the Gamma Team of Inria, focusing on theoretical results and demonstrations. The GammaO team involves researchers from Gamma (Inria) and ONERA and focuses on the transfer of the mesh adaptation technology to multi-physics:
  • aerodynamics including turbomachinery flow
  • plasmas including arc lightning
  • reentry, including wall heat flux on anisotropic tetrahedron grids

Cooperation: G. Barreau (ONERA/DPHY), F. Pechereau (ONERA/DPHY), F. Tholin (ONERA/DPHY), J. Vanharen (Inria), B. Maugars (DAAA/CLEF), C. Content (DAAA/CLEF), A. Loseille (INRIA/Gamma), F. Alauzet (INRIA/Gamma), C. Tarsia-Morisco (Inria), and engineers at Safran Tech.

High-order spectral discontinuous methods on unstructured grids

Many recent works focus on new numerical techniques based on the polynomial representation of quantities inside each mesh element and on special treatment for data discontinuity at cell interfaces. Among them, one famous approach is called the Discontinuous Galerkin approach. At Cerfacs, the development of a new solver based on the Spectral Difference method was initiated and the project is shared today between Cerfacs and ONERA. This solver is called JAGUAR.
  • After many efforts dedicated to High-Performance Computing (HPC), especially for LES, we are currently working on four axes: 1. the extension of the Spectral Difference Method to handle multielement meshes, 2. the development of a shock-capturing scheme, 3. the extension to multi-species reacting flows and 4. the definition of an efficient implicit time integration technique.
    Cooperation: Many colleagues from ONERA and CERFACS. Strong cooperation with A. Veilleux (former PhD Student, ONERA and CERFACS), R. Fievet (Former post-doc, RTRA and ONERA), H. Deniau (ONERA), A. Genot (ONERA), J-M. Senoner (ONERA), P. Seize (ONERA and DGA), J-F. Boussuge (CERFACS), G. Daviller (CERFACS), M. Montagnac (CERFACS).

  • Another activity is performed in the framework of the LMA2S lab. It concerns the transfer of the spectral difference method to deal with Maxwell's equation.
    Cooperation with many colleagues from ONERA. Joint work with X. Ferrieres (ONERA), S. Pernet (ONERA), P. Cantin (INSA) and V. Ritzenthaler (PhD Student, ONERA and INSA).

Time integration techniques

The time integration procedure is still one bottleneck of many physics. I was involved for a long time in the time spectral methods (Time Spectral method and Harmonic Balance method) for periodic and aperiodic flows. Today, I focus my research on methods for RANS and unsteady solutions (LES).
  • A still active research area concerns the definition of an efficient algorithm for the linearized treatment of the implicit system of equations in the framework of multi-physics simulations. Indeed, even if the definition of a linear solver to invert the linear system from the time discretization of the nonlinear initial problem is well-known, the standard definition of the matrix to invert deals with human experience to cancel or to model terms.
    Cooperation: P. Seize (PhD Student, ONERA) and L. Matuszweski (ONERA).

  • Another active research area concerns the development of time integration techniques for large time steps and dedicated to high-order spectral discontinuous methods.
    Cooperation: P. Seize (PhD Student, ONERA) and L. Matuszweski (ONERA).

Former and present Ph.D. students

  • V. Golliet, 2024-2027, Extension de la procédure de l'adaptation de maillage aux écoulements réactifs de la rentrée atmosphérique, advised by myself and co-advised by F. Alauzet.

  • Y. Gorschka, 2022-2025, Développement d'une approche volume fini node-centred pour l'adaptation de maillage anisotrope dans le solveur de CFD SoNICS, advised by myself, with involvement of B. Maugars (ONERA-DAAA), C. Content (ONERA-DAAA) and engineers from Safran Tech.

  • V. Ritzenthaler, 2021-2024, Couplage des différences spectrales avec une approche mimétique pour la prise en compte d'irrégularités de maillage dans la résolution des équations de Maxwell instationnaires, advised by X. Ferrieres (ONERA-DEMR) and P. Cantin (INSA), with involvement of S. Pernet (ONERA-DTIS) and myself.

  • G. Barreau, 2021-2024, Modélisation des arcs continus : application à la foudre et à la chambre à arc de F4, advised by F. Alauzet (INRIA GAMMA) and myself, co-advised by F. Pechereau (ONERA-DPHY).

  • P. Seize, Méthodologies permettant l’obtention efficace de solutions multi-physiques stationnaires pour des applications en énergétique, funded by DGA and ONERA, advised by myself and co-advised by L. Matuszweski (ONERA-DMPE), 2023.

  • A. Veilleux, Extension of the Spectral Difference method to simplex cells and hybrid grids, funded by ONERA and CERFACS, advised by myself and co-advised by G. Daviller (CERFACS), with involvement of H. Deniau, 2021.

  • L. Muscat, Coupling of time integration schemes for compressible unsteady flows, funded by ArianeGroup, advised by myself and co-advised by M. Montagnac (CERFACS), 2019.

  • C. Coreixas, High-order extension of the recursive regularized lattice Boltzmann method, funded by CERFACS' contract, advised by Jean-François Boussuge (CERFACS) and myself, 2018.

  • J. Vanharen, High-order numerical methods for unsteady flows around complex geometries, funding by Airbus, 2017.

  • C. Pérez Arroyo, Large eddy simulations of a dual stream jet with shock-cells and noise emission analysis, funded by Aerotranet-2 Marie-Curie fellow, advised by Prof. C. Airiau (IMFT) and co-advised by myself, 2016.

  • P. Cayot, Schémas numériques d'ordre élevé pour la simulation des écoulements turbulents sur maillage structuré et non structuré, funded by SCNEMA and CIRT, advised by myself, 2016.

Post-docs and engineer

  • G. Dufour (2006-2008), CERFACS, on harmonic balance technique for unsteady solution on deformable grids, now at ISAE-SupAero

  • G. Joubert (2007-2008), CERFACS, on research programs, now at Aero-Nautic Services & Engineering

  • N. Villedieu (2013-2015), CERFACS, on the development of JAGUAR, now at CONDOR SAS

  • S. Bidadi (2015-2016), CERFACS, on aeroacoustic simulations with shocks, now at the National Renewable Energy Laboratory at the University of Alabama

  • A. Balan (2015-2017), CERFACS, on the development of JAGUAR, now at the Department of Aerospace Engineering at the Indian Institute of Technology, Bombay

PhD defense committee

  • R. Simo Tamou, Développement de méthodes d’ordre élevé dans un solveur cartésien / AMR pour la modélisation de la combustion, 2025. Member.
  • F. Miralles, Simulation aérodynamique et aéroacoustique d’écoulements massivement décollés par des modèles de turbulence hybrides et de transition, 2023. Reviewer.
  • T. Jeanneau, Etude et validation d’une approche cinétique couplée pour la modélisation du transfert multimodal et multi-échelle de chaleur en milieu hétérogène, 2023. Reviewer.
  • L. Tallois, Simulation numérique de l'ablation liquide, 2023. Member.
  • S. Courtiaud, Étude et simulation de la postcombustion turbulente des explosifs homogènes sous-oxygénés, 2017. Member.
  • F. Blachère, Schémas numériques d'ordre élevé et préservant l'asymptotique pour l'hydrodynamique radiative, 2016. Member.
  • G. Georges, Développement d’un schéma aux volumes finis centré lagrangien pour la résolution 3D des équations de l’hydrodynamique et de l’hyperélasticité, 2016. Member.

Review and expertise

  • Journal of Computational Physics
  • Journal of Scientific Computing
  • AIAA Journal
  • International Journal of Computational Fluid Dynamics
  • Flow, Turbulence, and Combustion
  • Computers and Fluids
  • ASME Turbo Expo conference
  • Agence Nationale de la Recherche
  • PRACE computational resources


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