Topics of interest
- Numerical analysis
- High-order schemes
- Discontinuous Galerkin discretization
- Multidimensional Riemann solvers
- Monolithic methods
- Positivity preservation
- Entropic solutions
- Stability analysis (G-K-S theory)
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- Scientific computing
- Hyperbolic systems of PDEs
- Local subcell correction technique
- Gas dynamics
- Hypersonic flows
- Updated and total Lagrangian formalisms
- Solid dynamics in high deformations
- Inverse Lax-Wendroff boundary conditions
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Articles
S. Cardonna, F. Marche and F. Vilar,
Local subcell monolithic DG/FV scheme for 2D NSW on unstructured grids. Journal of Computational Physics, 2026.
Submitted, under reviewlink to pdf
S. Cardonna, A. Haidar, F. Marche and F. Vilar,
Local subcell monolithic DG/FV methods for nonlinear shallow-water models with source terms. Internat. J. for Num. Methods in Fluids, 2026.
Submitted, under reviewlink to pdf
F. Vilar,
Local subcell monolithic DG/FV convex property preserving scheme on unstructured grids and entropy consideration. Journal of Computational Physics, 521:113535, 2024.
link to pdf
A. Haidar, F. Marche and F. Vilar,
An ALE Numerical Method for the Waterline Evolution of a Floating Object with Non-linear Shallow-water Equations. Journal of Scientific Computing, 102(53), 2024.
link to pdf
A. Haidar, F. Marche and F. Vilar,
Free-boundary problems for wave-structure interactions in shallow-water: DG-ALE description and local subcell correction. Journal of Scientific Computing, 98, 45, 2024.
link to pdf
F. Vilar and R. Abgrall,
A posteriori local subcell correction of high-order discontinuous Galerkin scheme for conservation laws on two-dimensional unstructured grids. SIAM Journal on Scientific Computing, 46(2):A851 A883, 2024.
link to pdf
A. Haidar, F. Marche and F. Vilar,
A posteriori Finite-Volume local subcell correction of high-order discontinuous Galerkin schemes for the nonlinear shallow-water equations. Journal of Computational Physics, 452:110902, 2022.
link to pdf
F. Vilar,
A Posteriori Correction of High-Order Discontinuous Galerkin Scheme through Subcell Finite Volume Formulation and Flux Reconstruction. Journal of Computational Physics, 387:245-279, 2018.
link to pdf
F. Vilar, C.-W. Shu and P.-H. Maire,
Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: Form first-order to high-orders. Part II: The two-dimensional case. Journal of Computational Physics, 312:416-442, 2016.
link to pdf
F. Vilar, C.-W. Shu and P.-H. Maire,
Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: Form first-order to high-orders. Part I: The two-dimensional case. Journal of Computational Physics, 312:385-415, 2016.
link to pdf
F. Vilar, P.-H. Maire and R. Abgrall,
A discontinuous Galerkin discretization for solving the two-dimensional gas dynamics equations written under total Lagrangian formulation on general unstructured grids. Journal of Computational Physics, 276:188-234, 2014.
link to pdf
F. Vilar and C.-W. Shu,
Development and stability analysis of the inverse Lax-Wendroff boundary treatment for central compact schemes. ESAIM: Mathematical Modelling and Numerical Analysis, 49(1):39-67, 2014, 2014.
link to pdf
F. Vilar,
Cell-Centered Discontinuous Galerkin discretization for two-dimensional Lagrangian hydrodynamics. Computers and Fluids, 64:64-73, 2012.
link to pdf
F. Vilar, P.-H. Maire and R. Abgrall,
Cell-centered discontinuous Galerkin discretizations for two-dimensional scalar conservation laws on unstructured grids and for one-dimensional Lagrangian hydrodynamics. Computers and Fluids, 46(1):498-504, 2011.
link to pdf
PhD Thesis
A high-order discontinuous Galerkin discretization for solving two-dimensional Lagrangian hydrodynamics, supervised by Pierre-Henri Maire (CEA) and Rémi Abgrall (INRIA, IMB) at CELIA laboratory (Bordeaux, France) and at CEA-CESTA (Le Barp, France).
link to document link to slides
International conferences
HONOM 2024: High-Order NOnlinear numerical Methods for evolutionary PDEs, Xania, Greece, September 2024.
link to web site link to slides
ALGORITMY 2024: Central-European Conference on Scientific Computing, Podbanské, Slovakia, March 2024.
link to web site link to slides
CFC 2023: 22nd Computational Fluids Conference, Cannes, France, April 2023.
link to web site link to slides
Essentially hyperbolic problems: unconventional numerics, and applications, Monte Verità, Switzerland, October 2022.
link to web site link to slides
ECCM - ECFD 2018: Conference on Computational Methods in Applied Sciences, Glasgow, UK, June 2018.
link to web site link to slides
SHARK-FV: Sharing High-order Advanced Research Know-how on Finite Volume, Minho, Portugal, May 2018.
link to web site link to slides
ECCOMAS Young Investigators Conference, Milan, Italy, September 2017.
link to web site link to slides
SHARK-FV: Sharing High-order Advanced Research Know-how on Finite Volume, Ofir, Portugal, May 2017.
link to web site link to slides
USNCCM13: US National congress on computational mechanics, San Diego, USA, July 2015.
link to web site link to slides
WCCM XI - ECCM V - ECFD VI: Conference on Computational Methods in Applied Sciences, Barcelona, Spain, July 2014.
link to web site link to slides
MULTIMAT 2013: Conference on Numerical Methods for Multi-Material Fluid Flows, San Francisco, USA, Septembre 2013.
link to web site link to slides
ECCOMAS 2012: Conference on Computational Methods in Applied Sciences, Vienne, Autriche, Septembre 2012.
link to web site link to slides
MULTIMAT 2011: Conference on Numerical Methods for Multi-Material Fluid Flows, Arcachon, France, Septembre 2011.
link to web site link to slides
4
eme
Journée Calcul Scientifique de Toulouse: Conference on advanced numerical methods and their implementation, Toulouse, France, June 2010.
link to web site link to poster
ICFD 2010: Conference on Numerical Methods for Fluid Dynamics, Reading, Angleterre, Avril 2010.
link to web site link to poster
Seminars
EDP2 seminar, LAMA, Savoie Mont Blanc University, 2025.
link to slides
SISMA seminar, IRMA, LiHPC, Paris, 2025.
link to slides
CEA-SMAI/GAMNI: Numerical hydrodynamics seminar, IHP, Paris, 2025.
link to slides
Partial differential equations seminar, IRMA, Strasbourg University, 2024.
link to slides
Occitanie applied mathematics days, Perpignan University, 2023.
link to slides
ACSIOM seminar, Montpellier University, France, 2021.
link to slides
Scientific Computing and Modelization seminar, Bordeaux University, France, 2019.
link to slides
« Numerische Simulation » seminar, Koln University, Germany, 2019.
link to slides
PDE, Modelization and Scientific Computing seminar, Lyon University, France, 2019.
link to slides
Institute of Appl. Phys. and Comput. Math. seminar, Beijing, China, 2018.
Presentation 1/2 Presentation 2/2
ACSIOM seminar, Montpellier University, France, 2016.
link to slides
PDE Numerical Analysis, Nice University, 2015.
link to slides
Plasmas woking group, INRIA Sophia, France, 2015.
link to slides
Applied Mathematics Division, Brown University, Providence, USA, 2013 et 2014.
presentation 2013 presentation 2014
Teachings
Here are some of the courses that have mostly shaped my teaching activities in recent years. .
2021 - today
Numerical Analysis 1 & 2
1st year graduate students in Applied Mathematics in Montpellier University.
Class 1/4 Class 2/4 Class 3/4 Class 4/4
2019 - today
Lagrangian formalisms and compressible gas dynamics
2nd year graduate students in Applied Mathematics in Montpellier University.
Class text book
2025 - auj.
Mathematical tools for EEA students
2nd year undergraduate students in Electronics, Energy and Automation in Montpellier University.
2017 - today
Numerical analysis of ODEs
3rd year undergraduate students in Mathematics in Montpellier University.
2019 - 2024
TEE Mathematics
2nd year undergraduate students in Environment science in Montpellier University.
International teachings
2019
Analytical and numerical resolution of scalar conservation laws
Teaching in the frame of an EMA (African Mathematical School) under the aegis of the CIMPA at the « Institut National Polytechnique HB », Yamoussoukro, Ivory Coast.
Cours 1/5 Cours 2/5 Cours 3/5 Cours 4/5 Cours 5/5
PhD supervision
2023 - auj.
Sacha Cardonna
Applied Mathmetiques PhD supervision of Sacha Cardonna on the « Numerical analysis of free boundary problems and wave-structure interactions », in Montpellier University.
Applied Mathmetiques PhD supervision of Ali Haidar on the « Modelization and numerical simulation of non-linear shallow waters with a floating moving structure », in Montpellier University.
Thesis defended on the 2nd of Decembre 2022
Collective responsibilities
2025 - today
Section 26 committee - MIPS pole
Member of the section 26 (rank B) committee of the Mathematics, Computer Science, Physics and Systems (MIPS) pole in Montpellier.
2025 - today
Technology transfer contact at IMAG
Technology transfer contact person at the Institut Montpelliérain Alexander Grothendieck, Montpellier University.
2017 - today
AMIES contact
AMIES contact (Agency for Mathematics in Interaction with Enterprises and Society) in Montpellier.
2018 - 2021
GAMNI liaison committee
Member of the GAMNI liaison committee (Group for the Advancement of Numerical Methods for Engineering).
2017 - 2020
MSOc (Modélisation, Simulation et Optimisation en Occitanie)
IMAG lead (with B. Charlier, EPS team) for the set-up of MSOc in partnership with Toulouse University.
Scientific leadership and grants
2026 - today
PI of ANR project HYPERSONICS
ANR ASTRID project (358,210 €).
Project members: H. Beaugendre (Bordeaux Univ.), J.-P. Braeunig (CEA-CESTA), J. Jung (Pau Univ.), R. Loubère (Bordeaux Univ), P.-H. Maire (CEA-CESTA), V. Perrier (INRIA Pau), F. Vilar (Montpellier Univ.).
link to web site
2026 - today
Member of ANR project MSMPhi
ANR mono-team project (263,268 €).
PI: Matthieu Hillairet (Montpellier University).
link to web site
Organization activities
2022 - today
Organization of MULTIMAT 2026
Member of the organizing and scientific committees of MULTIMAT, September 2026, Biarritz, France.
link to web site
2022 - today
Scientific Committee of SHARK-FV
Member of the scientific committee of SHARK-FV conference, organized each year in Minho, Portugal.
link to web site
June 2016
Minisymposium · ECCOMAS Congress 2016
Co-organizer of the minisymposium « New trends in numerical methods for multimaterial compressible fluid flows » at ECCOMAS 2016.
2016 - 2020
ACSIOM seminar
Organizer of the weekly ACSIOM seminar at IMAG.
Professional experiences
Sept. 2016 - today
Associate professor · Montpellier University
Teaching Mathematics at Montpellier University, mainly on topics related to numerical analysis and scientific computing.
Researcher in the ACSIOM team at IMAG on divers problems related to the development and analysis of numerical schemes for the resolution of hyperbolic problems.
Mar. 2016 - July 2016
Research Engineer · Lyon University
Implementation of a discontinuous Galerkin (DG) computational code for the simulation of oceanographic flows, in collaboration with Daniel Le Roux, within the ICJ (Institut Camille Jordan)
Dec. 2012 - Nov. 2015
Postdoctoral Research Associate · Brown University
Discontinuous Galerkin and weighted essentially non-oscillatory (WENO) schemes for the simulation of compressible flows,
supervised by Chi-Wang Shu (Brown), funded by N.A.S.A., at Brown University (Providence, RI).
Education
Sept. 2009 - Nov. 2012
PhD Thesis · Bordeaux University
A high-order discontinuous Galerkin discretization for solving two-dimensional Lagrangian hydrodynamics,
supervised by Pierre-Henri Maire (CEA) and Rémi Abgrall (INRIA, IMB) at the CEA Cesta (Le Barp). Defended November the 16th 2012.
Sept. 2006 - July 2009
Engineering School · MATMECA
ENSEIRB-MATMECA enginnering school of the Institut Polytechnique de Bordeaux (IPB). Physical phenomena simulation, partial differential equations,
numerical analysis, solids and fluids mechanics, structure analysis, aerodynamics, parallel programming.
June 2009
Master's degree · Bordeaux University
Scientific computing and numerical analysis.
June 2007
Bachelor in Mathematics · Bordeaux University
Engineering Mathematics.
Sept. 2004 - June 2006
Classes préparatoires · CpBx
Mathématics / Physics.
