Paul VIGNEAUX
Professeur à l'Université de Picardie Jules Verne, membre du LAMFA CNRS UMR 7352
Membre associé de l'Unité de mathématiques pures et appliquées CNRS UMR 5669 ENS de Lyon


⚟ Porteur du projet ANR VPFlows (2021-2026) : web site

⚟ Responsable de l'Axe (ex. GdR) "Géophysique et risques naturels" du Réseau Thématique CNRS "Terre & Énergies" : web site (création le 1.1.2024)

⚟ Responsable de l'équipe d'Analyse Appliquée du LAMFA


Responsabilités récentes :
2022-2023 : Directeur du GdR CNRS MathGeoPhy (web site) du 1.1.2022 au 31.12.2023. Artisan de la création du RT "Terre & Énergies" avec A. Ern et N. Seguin en 2023, suite à la fusion des GdRs en RT par le CNRS Mathématiques.
2021-2022 : Lyon ED Info-Math: Conseil et Commission des thèses (~340 doctorants)
2019-2021 : Co-Responsable Scientifique du GdR CNRS EGRIN et mission de construction de MathGeoPhy
2019-2021 : Responsable du Master 1 de mathématiques, ENS de Lyon (2 ans de Covid : compte double)

Brief bio

I am a full professor of mathematics at Université de Picardie, Amiens, since Sept 2022. I was Associate Professor at the École Normale Supérieure de Lyon between 2008 and 2022, at the UMPA.

• Habilitation à diriger des Recherches (HDR) from ENS de Lyon: June 2017.
• Qualified for full prof. positions since 2018.
• Academic year at UBC, Vancouver 2018-2019 (Délégation CNRS @ PIMS).
• CNRS Postdoctoral fellow, 2007-2008. LAMA, Chambéry.
• Member of the INRIA NUMED team during the lifetime of the project : 2008-2021.
• PhD degree in applied mathematics at the Institute of Mathematics of Bordeaux (IMB) in 2007.

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, test of an avalanche in the Taconnaz path, Chamonix - Mont-Blanc: Movie link on HAL (if not compatible with current web browser, it can be downloaded and viewed with ad hoc movie player) or iframe (if compatible, e.g. with chrome browser):



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:

• PDE models and their HPC simulations
• Inverse problem/Parameters estimation via Bayesian methods: in particular we focus on SAEM methods and their coupling with PDEs. We use metamodelling like kriging to speed-up computation times of these complex models (e.g. our SAEM+Kriging method). Methodological papers: 2014, 2016.
• 3D MRI time series: treament and analysis; segmentation of evolving fronts (e.g. tumour growth)
• Implementation tools used: F90, C++, MPI, Python (and Matlab), FreeFem++, VTK, ITK, PyQT, etc

▲ 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.

Communications

Publications and Preprints

Submitted

• Image parametrization of low grade glioma using a level surface model. under review. P. Vigneaux, V. Louvet, E. Maguet, A. Pieters, F. Ducray, E. Grenier.

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

• On stability condition for bifluid flows with surface tension : application to microfluidics. Journal of Computational Physics, 2008, 227 (12), pp. 6140-6164. Preprint HAL With: Cédric Galusinski.
• A mathematical model for mechanotransduction at the early steps of suture formation. Proceedings of the Royal Society of London. Series B. 2013, 280(1759) DOI Preprint HAL(Main text and Suppl. material in the same PDF). With: R. H. Khonsari, J. Olivier, S. Sanchez, P. Tafforeau, P. E. Ahlberg, F. Di Rocco, D. Bresch, P. Corre, A. Ohazama, P. T. Sharpe and V. Calvez.

Numerical Analysis and Visco-Plastic flows

• A metamodel for confined yield stress flows and parameters' estimation. Rheologica Acta, February 2024. Code repository (Zenodo). Preprint HAL. Preprint arXiv. DOI. Springer link. With: Clément Berger and David Coulette
• Multilayer models for hydrostatic Herschel-Bulkley viscoplastic flows. Computers and Mathematics with Applications, June 2023, Vol. 139, pp 99-117. Preprint HAL. DOI. With: E. D. Fernández-Nieto and José Garres-Díaz
• Confined yield stress lubrication flows for cement paste backfill in underground stopes. Cement and Concrete Research, February 2023, Vol. 164, p. 107038. With: Y. Shao and I. Frigaard. Preprint HAL. DOI.
• Flow of a yield-stress fluid over a cavity: experimental and numerical investigation of a viscoplastic boundary layer. Journal of Non-Newtonian Fluid Mechanics, 2018, Vol. 261, pp 38-49. Preprint HAL With: G. Chambon, A. Marly, L.-H. Luu and P. Philippe.
• Efficient numerical schemes for viscoplastic avalanches. Part 2: the 2D case. Journal of Computational Physics, 2018, Vol. 353, pp 460-490. Preprint HAL With: Enrique D. Fernández-Nieto and Jose M. Gallardo.
• Augmented Lagrangian simulations study of yield-stress fluid flows in expansion-contraction and comparisons with physical experiments. Journal of Non-Newtonian Fluid Mechanics, 2017, Vol. 239, pp. 35-52. Preprint HAL With: Arthur Marly.
• Efficient numerical schemes for viscoplastic avalanches. Part 1: the 1D case. Journal of Computational Physics, 2014, Vol. 264, pp 55-90. Preprint HAL With: Enrique D. Fernández-Nieto and Jose M. Gallardo.
• A well-balanced finite volume-augmented Lagrangian method for an integrated Herschel-Bulkley model. Journal of Scientific Computing, 2012, 53 (3), pp. 608-641. Preprint HAL With: C. Acary-Robert, E. D. Fernández-Nieto and G. Narbona-Reina.
• Augmented Lagrangian Method and Compressible Visco-Plastic Flows: Applications to Shallow Dense Avalanches. Advances in Mathematical Fluid Mechanics, 2010, New Directions in Mathematical Fluid Mechanics, pp. 57-89. Preprint HAL With: D. Bresch, E. D. Fernández-Nieto and I. Ionescu.

PDEs and Statistics

• Population parametrization of costly black box models using iterations between SAEM algorithm and kriging. Computational and Applied Mathematics, 2018, Vol. 37(1), pp. 161-173 (accepted March 2016). Preprint HAL With: Emmanuel Grenier, Céline Helbert, Violaine Louvet and Adeline Samson.
• Parameter estimation in non-linear mixed effects models with SAEM algorithm: extension from ODE to PDE. ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 2014, 48(5), pp. 1303-1329. Preprint HAL With: Emmanuel Grenier and Violaine Louvet.

HAL profile (publications, updated version of articles, etc), Google Scholar, IdRef : 119020149, theses.fr and

Some Conferences and Workshops

References can also be found on HAL.

Invited lectures in Ph.D. programs

• Microfluidics, Nanofluidics: ounces of physics, modelling & numerical methods. 13th CNRS Thematic School on Computational Fluid Dynamics (MFN). June 2-8, 2013. Abstract
• Duality methods for variational inequalities and Non-Newtonian fluid mechanics. Doctoral course at the Institute of Mathematics of Seville (IMUS). October, 2013. Slides used as an introduction to Rheology.
• Small scale fluid dynamics, interfaces and numerics. PhD lecture at the 20th CEMRACS Summer School. July 20 - August 28, 2015. CIRM, Marseille. Abstract and Slides

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) :

• IMB - Equipe de Mathématiques Appliquées (MAB)
• Equipe-Projet INRIA : MC2
• Collaboration avec le LOF, unité Rhodia-CNRS à Bordeaux (aujourd'hui Solvay-CNRS)
  

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

(Among others)

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).

Invitation to the launching of the national "Institute of Mathematics for Planet Earth" (IMPT). November 2021.

Invitation to "Soirées Mathématiques de Lyon" (SML). December 2021

Ph.D. student supervisions

(and also Ph.D. committees) listed here: theses.fr

Arthur Marly defended his thesis on Sept 19th, 2018. Abstract. AGPR at ENS de Lyon (2018-2021). Professeur Agrégé, French Preparatory Classes since 2021.

Clément Berger @ UMPA - ENS de Lyon. PhD Grant élève normalien. 2021-

Colin Ginot @ INRAE. PhD Grant ANR. 2021-. Co-advised (15%) with Guillaume Chambon (INRAE Grenoble) and Pierre Philippe (INRAE Aix)

Maxime Wallon @ LAMFA - UPJV. PhD Grant ANR. 2022-. Co-advised (50%) with Pierre Saramito (LJK Grenoble)

Pei Sun @ LAMFA - UPJV. PhD Grant CNRS (MiTi project Strudel3D). 2024-. Co-advised with Alejandro Franco (LRCS) and Jean-Paul Chehab (LAMFA)

Contact

LAMFA - CNRS UMR 7352
Université de Picardie Jules Verne
33, rue Saint Leu
F-80039 Amiens Cedex 1 - France

Tel : (33/0) 3 22 82 78 48

Courrier électronique :

Last updated: Jan 2024