Maître de conférences HDR à l'École Normale Supérieure de Lyon - Unité de mathématiques pures et appliquées CNRS UMR 5669
Membre de l'équipe INRIA NUMED

Porteur du projet ANR VPFlows (2021-2025) : web site

Co-Responsable Scientifique du GdR CNRS EGRIN

Responsable du Master 1 de mathématiques, ENS de Lyon

Brief bio

I am an associate professor (HDR) of mathematics at the École Normale Supérieure de Lyon since 2008.

My research is dedicated to numerical analysis of PDE's, scientific computing and simulation in fluid mechanics and medicine.

In The Gallery ⛏▝

Viscoplastic fluids: avalanches, free surfaces. Here (time evolution from left to right, top to bottom) test of an avalanche in the Taconnaz path, Chamonix - Mont-Blanc: Animated GIF

We use specially designed duality and well-balanced finite volume schemes (Paper, to be read with this one too).

Viscoplastic fluids: Bingham model with duality methods, like Augmented Lagrangian (no regularisation)

HPC (MUMPS-MPI) for highly resolved yield interface in expansion-contraction (Paper) ...

... and its use for boundary layers in cavities, Oldroyd theory revisited (Paper):

Numerical modelling in Medicine:

We blend a wide spectrum of methods to deal with data of our Physicians colleagues (Oncologists, etc). It includes:

Craniofacial Suture digitation at early stage - Mechanotransduction: Model description and illustration of the instability. Assessment of the results(a-d. Simulations with FreeFem++): (b) stress (c) fibers orientation (d) mesenchymal cell density and pattern of bone deposition. Inspired by incredible 3D imaging of various specimens done at the European Synchrotron Radiation Facility (ESRF, Grenoble, France) for this study, including Polypterus bichir (last picture). Right-click to enlarge pictures. 2009-2012 Paper

Microfluidics, Level Sets and Droplet's dynamics: creation and various mixing regimes. Insight on the discretisation' stability condition for "capillary flows". 2004-2007 Paper

▝ Title of this section courtesy of Dire Straits.


Publications and Preprints

Updated references and plain texts can be found on the Open Archives Repository: HAL.

Numerical Analysis and Visco-Plastic flows PDEs and Statistics
HAL profile (publications, updated version of articles, etc), Google Scholar and

Some Conferences and Workshops

References can also be found on HAL.

A list of all communications by year thanks to HAL-INRIA tools: list

Invited lectures in Ph.D. programs

Ph.D. / Thèse

Paul Vigneaux, Level Set methods for free-boundary problems in Microfluidics / Méthodes Level Set pour des problèmes d'interface en microfluidique, Université Bordeaux 1, 2007. Manuscrit sur TEL.

Cadre institutionnel (de 2004 à 2007) :

Habilitation (HDR)

Contributions à des problèmes viscoplastiques et d'estimation de paramètres, ENS de Lyon, 22 Juin 2017.
Jury :
Rapporteurs : Christophe Ancey (EPFL, Suisse), Alfredo Bermúdez (U. de Santiago de Compostela, Espagne), Jean-Paul Vila (IMT & INSA, Toulouse).
Examinateurs : François Bouchut (CNRS & U. Paris-Est), Emmanuel Grenier (ENS de Lyon), Laure Saint-Raymond (ENS de Lyon).
Résumé. Manuscrit sur TEL.

Public Awareness

Contributions to "Images des Mathématiques" (in French).
Including a translation in French of a series of European "Success stories" of Mathematics in the Industry. These were published by a "Forward Look" of the ESF and the EMS, see here for all the details.

Contribution to the daily blog of the 2013 UNESCO "Mathematics of Planet Earth" Initiative (in French). "Neige de printemps et avalanches" (June 2013). Now part of the book "Brèves de Maths" (Nouveau Monde éditions, 2014)

Ph.D. student supervision

Arthur Marly defended his thesis on Sept 19th, 2018. Abstract. He is now AGPR at ENS de Lyon.


ENS de Lyon
(Site Sciences)
46, allée d'Italie
69364 Lyon Cedex 07 - France

Tel : (33/0) 472 72 85 45
Fax : (33/0) 472 72 84 80

Courrier électronique :

Last updated: Oct. 2020