Hélène Mathis

Professeure

Université de Montpellier

Institut Montpellierain Alexander Grothendieck, UMR 5149

                IMAG

I work at the Institut Montpellierain Alexander Grothendieck and was previously at the Laboratoire de Mathématiques Jean Leray of Nantes Université. My research concerns the numerical approximation of hyperbolic systems. My favorite applications are the modelling of complex compressible multiphase flows.

Key words

  • Modelling of complex flows, compressible multiphase flows, interface, liquid-vapor phase change, nuclear safety applications, liquid-solid phase transition arising in geophysics problems
  • Hyperbolic systems, relaxation, multiscale problems, relative entropy technics
  • Numerical analysis Finite Volume schemes, Asymptotic preserving schemes, coupling and adaptative techniques, interface


My CV (fr) is available here (last update: April 2022).

Research

Students and postdoc

Scientific projects

Publications

Habilitation à diriger des recherces

Entropie en dynamique des fluides, defended the 7th of December 2020, Nantes, HAL

Preprint

  1. Analysis of compressible bubbly flows. Part 1: construction of a microscopic model , soumis, HAL
    with M. Hillairet and N. Seguin
  2. Analysis of compressible bubbly flows. Part 2: derivation of a macroscopic model , soumis, HAL
    with M. Hillairet and N. Seguin
  3. Simulation of an homogeneous relaxation model for a three-phase mixture with miscible phases , soumis, HAL
    with J. Bussac
  4. An asymptotic preserving scheme for hyperbolic problems with diffusive limit on bounded domain
    with N. Therme
  5. Relaxation models of phase transition flows accounting for surface tension
    In preparation
  6. Derivation of an immiscible two-phase flow from a kinetic formulation
    with B. Grec and F. Hérau
    In preparation

Articles in peer-reviewed journals

  1. Numerical analysis of DDFV schemes for semiconductors energy-transport models, with M. Bessemoulin-Chatard and G. Lissoni
    Accepted in Computational and Applied Mathematics, 2021 HAL
  2. Analysis of numerical schemes for semiconductors energy-transport models with M. Bessemoulin-Chatard and C. Chainais-Hillairet
    Applied Numerical Mathematics, 168, pp.143-169, 2021, HAL
  3. Vapour-liquid phase transition and metastability, with H. Ghazi and F. James
    Discrete & Continuous Dynamical Systems -B, Volume 22, 2020, HAL
  4. A three-phase flow model with two miscible phases, with J.-M. Hérard
    ESAIM Math. Model. Numer. Anal., Volume 53 (4),pp. 1373--1389, 2019, HAL
  5. A thermodynamically consistent model of a liquid-vapor fluid with a gas
    ESAIM: M2AN, Volume 53 (1), pp. 63-84, 2019, HAL
  6. Modelling binary alloy solidification by a random projection method with S. Carpy
    Numerical Methods for Partial Diffrential Equations, Volume 35(2), 2018, Preprint
  7. A relaxation model for liquid-vapor phase change with metastability with F. James
    Communications in Mathematical Sciences, Volume 14(8), 2016, HAL
  8. Numerical convergence rate for a diffusive limit of hyperbolic systems : p-system with damping, with C. Berthon and M. Bessemoulin-Chatard
    SMAI J. of Comput. Math., Volume 2, 2016, HAL
  9. Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws, with C. Cancès and N. Seguin
    SIAM Journal on Numerical Analysis (SINUM), Volume 54(2), 2016, HAL
  10. Error analysis of a dynamic model adaptation procedure for nonlinear hyperbolic equations, with C. Cancès, F. Coquel, E. Godlewski and N. Seguin
    Communications in Mathematical Sciences, Volume 14(1), 2016, HAL
  11. Dynamic model adaptation for multiscale simulation of hyperbolic systems with relaxation with C. Cancès, E. Godlewski, N. Seguin
    Journal of Scientific Computing, Volume 63(3), 2015, HAL
  12. Random sampling remap for compressible two-phase flows with M. Bachmann, P. Helluy, J. Jung and S. Müller
    Computers and Fluids, 86 (2013), 275-283, HAL
  13. A well balanced approximate Riemann solver for compressible flows in variable cross-section ducts, with P. Helluy and J.-M. Hérard
    J. Comput. Appl. Math., 236, no. 7, 1976-1992, 2012, HAL
  14. Pressure laws and Fast Legendre Transform, with P. Helluy
    Math. Models Methods Appl. Sci., 21, no. 4, 745-775, 2011, HAL
  15. A simple parameter-free entropy correction for approximate Riemann solvers, with P. Helluy, J.-M. Hérard and S. Müller
    Comptes Rendus Mécanique, 338, no. 9, 493-498, 2010, HAL

Proceedings

  1. Numercial schemes for semiconductors energy-transport models, with M. Bessemoulin-Chatard and C. Chainais-Hillairet, H. Mathis
    Finite volumes for complex applications. IX, 2020, HAL
  2. Admissible equations of state for immiscible and miscible mixtures, with G. Faccanoni
    ESAIM Proc.Surveys, 66, 2019 HAL
  3. Vapour-liquid phase transition with metastability, with H. Ghazi and F. James
    ESAIM Proc.Surveys, 66, 2019 HAL
  4. Numerical convergence for a diffuse limit of hyperbolic systems on bounded domain, with N. Therme
    Finite volumes for complex applications. VIII, 2017
  5. Approximation d'interface liquide-solide dans l'hydrosphère de Ganymède par un schéma de type Glimm, with S. Carpy
    Rencontres du non linéaire, 2016
  6. Modeling phase transition and metastable phases, with F. James
    Finite volumes for complex applications. VII. Problems and perspectives, HAL
  7. OSAMOAL : Optimized Simulations by Adapted MOdels using Asymptotic Limits, with A.-C. Boulanger, C. Cancès, K. Saleh and N. Seguin
    ESAIM: Proc. Volume 38, pages 183-201, 2012, HAL
  8. Model adaptation for hyperbolic systems with relaxation, with N. Seguin
    Finite volumes for complex applications. VI. Problems and perspectives.
    Volume 1, 2, 673-681, Springer Proc. Math., 4, Springer, Heidelberg, 2011
  9. A simple model for cavitation with non-condesable gases, with M. Bachmann, P. Helluy and S. Müller
    13th Int. Conference on Hyperbolic Problems, 2010, HAL
  10. A well-balanced approximate Riemann solver for variable cross-section compressible flows, with P. Helluy and J.-M. Hérard
    AIAA paper 2009-3540, http://www.aiaa.org, 2009
  11. A local time-stepping discontinuous Galerkin algorithm for the MHD system, with C. Altmann, T. Belat, M. Gutnic, P. Helluy and E Sonnendrücker
    ESAIM, Proc. 28, pp. 33-54, 2009, HAL
  12. An ALE averaging approach for the computing of bubble oscillations, with P. Helluy and S. Müller
    Finite Volume for Complex Applications V. ISTE and Wiley, pp. 487-494, 2008

PhD Thesis

Étude théorique et numérique des écoulements avec transition de phase, defended the 29th of September 2010, Strasbourg, HAL

Conferences

Organization (member of the organization committee, recent events)

09/2022   New trends in complex flows, Paris
03/2022   Méthodes numériques pour des modèles multi-échelles, Pornichet
06/2021   Mini-symposium SMAI, modèles et schémas numériques pour les écoulements multi-constituants
06/2019   Numerical methods for multiscale models arising in physics and biology, Nantes
05/2019   SMAI, Guidel
01/2019   Rencontre LMJL-IFSTTAR, Agence Lebsegue
07/2018   Ecole du GdR MANU, Roscoff
02/2018   Cloture de l'ANR Achylles, Bordeaux
11/2017   Journées multiphasiques et incertitudes, Nantes
01/2017   Journée d'accueil en Mathématiques, Paris
06/2016   Ecole du GdR Egrin, Piriac-sur-Mer

Presentations

  • Habilitation à Diriger les recherches, slides
  • A three-phase mixture model, slides
  • Binary alloy solidification and random projection method (fr), slides

Some (recent) talks

05/2022   Séminaire Equations aux Dérivées Partielles et Applications, Nancy
04/2022   Séminaire de l'équipe ACSIOM, Montpellier
01/2022   34ème séminaire CEA/GMANI de mécanique des fluides numérique, Paris
01/2022   Seminar of Multiphase Flows, Institüt für Thermodynamik der Luft, Stuttgart
06/2021   Séminaire de l'équipe MACS, Nantes
10/2020   Journée d'Analyse Appliquée de la Fédération Mathématique, Lille des Hauts-de-France
07/2019   ICIAM 2019, mini-symposium Mathematical and numerical modelling of compressible multiphase flows - Part 2, Valencia
05/2019   Compressible Multiphase Flows : derivation, closure laws and thermodynamics, Strasbourg
05/2019   Mini-symposium Modélisation, analyse et simulation d'écoulements multiphasiques compressibles, congrès SMAI 2019, Guidel
01/2019   Rencontre LMJL-IFSTTAR, Nantes
01/2019   Séminaire de modélisation et calcul scientifique, Lyon
05/2018   Compressible Multiphase Flows : derivation, closure laws and thermodynamics, Strasbourg
12/2017   Groupe de travail, ENS Rennes
11/2017   Finite volume schemes and traffic Modeling in Besançon
10/2017   Multiphase 2017, Paris
06/2017   ETSN (école CEA), Cadarache
03/2017   Journées Volumes Finis, Nice
12/2016   Numerical Modeling of Liquid-Vapor Interfaces in Fluid Flows, Paris
06/2016   ABPDE II, Lille
05/2016   Séminaire d'analyse numérique, Orsay
05/2016   Groupe de Travail Manon, Paris
03/2016   Rencontres du non linéaire, Paris
01/2016   Groupe de Travail Entropie, Nantes

Teaching (Fr)

2022-2023

  • Les étudiants inscrits aux enseignements suivants peuvent récupérer les documents sur Moodle.


Méthodes des éléments finis, M1 MANU
Complément de Mathématiques, CPES
Mathématiques 2, CM, TD, TP, L1 PEIP

Responsabilité

Entre 2016 et 2020, j'ai été responsable du Master Modélisation, Analyse numérique et Calcul Scientifique (MACS) de l'Université de Nantes avec François Jauberteau.

C.V.

My CV (fr) is available here (last update: 08/2021)

Professional career

Since 2022   Professor, Université de Montpellier, Institut Montpellierain Alexander Grothendieck
2011-2022   Assistant professor, Université de Nantes, Laboratoire de Mathématiques Jean Leray
2010-2020   Post-doctoral position, Université Paris 6, Laboratoire Jacques-Louis Lions

2019       Associate researcher CNRS (délégation, 6 months)
2016       Associate researcher CNRS (délégation, 6 months), Laboratoire de Planétologie et Géodynamique

Training and diplomas

2020/12/07  Habilitation à Diriger les Recherches, Université de Nantes
          Entropie en dynamique des fluides
2010/09/30  PhD Thesis, Université de Strasbourg
          Etude théorique et numérique des écoulements avec transition de phase

Administrative responsabilities (fr)

01/2022 - 08/2022     Directrice de l'Agence Lebesgue
11/2021 - 08/2022     Membre élue du Conseil des Etudes de l'UFR Sciences et Techniques, Nantes
10/2021 - 08/2022     Correspondante de l'Agence Henri Lebesgue pour le LMJL
01/2021 - 08/2022     Membre nommée du Bureau du Laboratoire de Mathématiques Jean Leray
09/2020 - 08/2022     Membre élue du Conseil du Département de Mathématiques, Nantes

Quelques responsabilités passées

2016-2020      Responsable du Master Modélisation, Analyse numérique, Calcul Scientifique (MACS), Nantes
2014-2020      Membre du Conseil de Perfectionnement des Masters de Mathématiques, Université de Nantes
2014-2016      Correspondante AMIES et SMAI pour le LMJL
2013-2014      Membre élue du Conseil Scientifique de l'UFR Sciences et Techniques, Nantes
2013-2014      Membre élu du Conseil du Département de Mathématiques, Nantes

Comités de sélection

Campagne 2021      Poste MCF, section 25/26, Montpellier
Campagne 2020      Membre du comité CRCN INRIA
Campagne 2020      Poste PRAG, Nantes
Campagne 2019      Présidente de deux comités MCF, section 27, Nantes
Campage 2017     Poste PRAG, Nantes
Campage 2016     Poste PRAG, Nantes
Campagne 2015      Poste MCF, section 26, INSA Toulouse
Campagne 2013      Deux postes MCF, section 26, Nantes et Nancy

Contact

Email

helene.mathis[at]umontpellier.fr

Phone

(+33) 04 67 14 48 31

Postal address

IMAG, Université de Montpellier

Case courrier 051

Place Eugène Bataillon

34090 Montpellier, France

Office

Room 407

Building 9

How to get there