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About Me


I am currently associate professor at the Université de Toulon (UTLN) and do my research at the Institut Mathématiques de Toulon (IMATH) -Équipe de Modélisation Numérique (MN) . My fields of specialization and research interests include Non linear analysis of PDEs, Numerical analysis in fluid mechanics. Before joining the team MN, I was a postdoctoral researcher at the Basque Center for Applied Mathematics, Derio, Spain, directed by/in collaboration with Enrique Zuazua. I obtained my Ph.D in Applied Mathematics at the Laboratoire de Mathématiques-LAMA under the supervision of Christian Bourdarias & Stéphane Gerbi, Université de Savoie, Chambéry, France in 2010.
I deliver Scientific Computing and Numerical Analysis courses at the Ecole d'Ingénieurs de l'Université de Toulon which offers the possibility to get high level skills.

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Research


My fields of specialization and research interests include non linear analysis of Partial Differential Equations, Numerical Analysis and Computer Simulation. More precisely, I'm interested in the model reduction, the analysis, the construction of Finite Volume methods and the (multi-dimensional) numerical simulation of hyperbolic problems arising in fluid mechanics, especially for shallow water flows. A typical example is the well-known Saint-Venant equations which has a wide range of applications in real life problems.

I advise or advised the PhD of
Mohammed Ali Debyaoui (Nov. 2016 – 11 Dec. 2020), Applied Mathematics, "Contribution à la modélisation mathématique et numérique pour des modèles d'écoulement non-linéaires dispersifs en eaux peu profondes"
Jean-Baptiste Clément (Nov. 2017 – 11 Jan. 2021), Fluids Mechanics, "Numerical simulation of flows in unsaturated porous media by an adaptive discontinuous Galerkin method: application to sandy beaches"
Camille Poussel (Oct. 2021– ), Fluids Mechanics, "Modeling and numerical simulation of flow dynamics in sandy beaches"
Yolhan Mannes (Oct. 2021– ), Applied Mathematics, "Derivation, mathematical and numerical analysis of models for the cardiovascular system"

• You can find the list of my publications herein or on Arxiv, Mathscinet or Zentralblatt.
• You can also find my Math Genealogy Un smiley and the PDF file.

Modeling

Compressible and incompressible flows for shallow water flows, etc

Analysis

Well-posedness, asymptotic behavior, model reduction, etc

Numerical analysis

Finite volume scheme, high order scheme, well-balanced scheme, etc

Numerical simulation (CFD)

AMR, Mesh refinement criterion, Mesh refinement threshold, parallelization, etc

Recent results Dissemination activities

Dissemination activities


Related publications

  1. M. Ersoy, On a new mathematical model for open channel and river hydraulics. Download PDF
    2021-12-09 Colloque Modèles asymptotiques et méthodes numériques pour les milieux continus et la biologie, Saint-Etienne, France
  2. M. Ersoy, On a new mathematical model for open channel and river hydraulics. Download PDF
    2021-11-16 IMAG, ACSIOM, Montpellier, France
  3. M. Ersoy, Mathematical Modeling and numerical simulation for shallow water equations. PART 2: An atypical finite volume scheme.
    2021-01-29 Master Class: Applied Mathematics CEPS, CIRM, Marseille (LIEN)
  4. M. Ersoy, Mathematical Modeling and numerical simulation for shallow water equations. PART 1: Generalities. Download PDF
    2021-01-29 Master Class: Applied Mathematics CEPS, CIRM, Marseille (LIEN)
  5. M. Ersoy, From hydrostatic to non-hydrostatic models in fluid mechanics: modeling, mathematical and numerical analysis, and computational fluid dynamics. Download PDF
    2020-12-01 HDR, IMATH, La Garde, France ( https://bbb.univ-tln.fr/b/ers-8xf-ubd-bpg )
  6. M. Ersoy, Generalised Serre-Green-Naghdi equations for open channel and for natural river hydraulics. Download PDF
    2020-10-20 CMI, Marseille, France
  7. M. Ersoy, A new dispersive model for open channel and river flows Download PDF
    2019-06-21 Numerical methods for hyperbolic problems 2019, Malaga, Spain, 16-22 June 2019
  8. M. Ersoy, (poster) A new dispersive model for open channel and river flows Download PDF
    2019-05-13 International Workshop on Nonlocal Models, PDEs and Applications, Caen, France, May 13-14, 2019
  9. M. Ersoy, A kinetic scheme for air entrainment in transient flows: a two-layer approach. Download PDF
    2017-02-17 Dynamics and modeling of complex networks, 11èmes Journées Scientifiques de l’Université de Toulon, 25-26 April 2017, Toulon, France
  10. M. Ersoy, Adaptive mesh refinement method : numerical density of entropy production and automatic thresholding. Download PDF
    2017-02-17 University of Savoie Mont-Blanc, Chambéry, France
  11. M. Ersoy, An extended Saint-Venant system for urban flows. Download PDF
    2015-12-16 University of L'Aquila, Italy
  12. M. Ersoy, An extended Saint-Venant system for urban flows. Download PDF
    2015-12-15 13-18 December, La Sapienza, Italy
  13. M. Ersoy, Block-Based Adaptive Mesh Refinement scheme based on numerical density of entropy production for conservation laws and applications. Download PDF
    2015-06-11 International meeting AMS/EMS/SPM, Partial Differential Equations: Ambitious Mathematics for Real-life Applications, 10-13 June, Porto, Portugal
  14. M. Ersoy, A pressurized model for compressible pipe flows: derivation including friction. Download PDF
    2014-11-27 IMATH, Toulon, 2014
  15. M. Ersoy, On the numerical entropy production as a useful mesh refinement parameter: application to wave-breaking. Download PDF
    2014-10-02 IRMAR, Rennes, France
  16. M. Ersoy, On the numerical entropy production as a useful mesh refinement parameter: application to wave-breaking. Download PDF
    2014-09-16 CMI, Marseille, France
  17. M. Ersoy, On the numerical entropy production as a useful mesh refinement parameter: application to wave-breaking. Download PDF
    2014-07-(22-26) University of Sussex, GB, 22 - 26 July 2014
  18. M. Ersoy, On the numerical entropy production as a useful mesh refinement parameter: application to wave-breaking. Download PDF
    2014-07-17 The Third BCAM Workshop on Computational Mathematics, BCAM (Bilbao), July 17-18, 2014
  19. M. Ersoy, A pressurized model for compressible pipe flows: derivation including friction. Download PDF
    2014-05-12 Workshop MTM, BCAM (Bilbao), June 12-13, 2014
  20. M. Ersoy, Compressible primitive equations. Download PDF
    2014-04-16 8èmes journées scientifiques de l'Université de Toulon, France
  21. M. Ersoy, Air entrainment in transient flows in closed water pipes: A two-layer approach. Download PDF
    2013-06-18 Journées NTM, Porquerolles, France
  22. M. Ersoy, Shallow water equations: modeling, numerics and applications. Download PDF
    2013-(03-06)-06 University of Sussex, GB, 3 - 8 June 2013
  23. M. Ersoy, Adaptive multi scale scheme based on numerical density of entropy production for conservation laws. Download PDF
    2013-06-06 University of Sussex, GB, 3 - 8 June 2013
  24. M. Ersoy, Adaptive multi scale scheme based on numerical density of entropy production for conservation laws. Download PDF
    2013-06-31 5th Women in Mathematics Summer School on Mathematical Theories towards Environmental Models, ICTP, Trieste, Italy, 27 May - 1 June 2013
  25. M. Ersoy, Adaptive multi scale scheme based on numerical density of entropy production for conservation laws. Download PDF
    2013-02-18 Workshop MTM2011-29306, BCAM (Bilbao), February 18-19, 2013
  26. M. Ersoy, Adaptive multi scale scheme based on numerical density of entropy production for conservation laws. Download PDF
    2012-06-12 Journées NTM, Porquerolles, France
  27. M. Ersoy, Existence and stability results for some compressible primitive equations. Download PDF
    2011-12-15 IMATH, Toulon, France
  28. M. Ersoy, A Finite Volume Kinetic (FVK) framework for unsteady mixed flows in non uniform closed water pipes. Download PDF
    2011-11-24 IMATH, Toulon, France
  29. M. Ersoy, (poster) NUMERIWAVES Project ERC FP7 - 246775 New analytical and numerical methods in wave propagation Download PDF
    2011-07-05 OPTPDE - Summer School - Challenges in Applied Control and Optimal Design, July 4-8, 2011
  30. M. Ersoy, A Well Balanced Finite Volume Kinetic (FVK) scheme for unsteady mixed flows in non uniform closed water pipes. Download PDF
    2011-03-31 LM UBP, Clermont-Ferrand, France
  31. M. Ersoy, A Well Balanced Finite Volume Kinetic (FVK) scheme for unsteady mixed flows in non uniform closed water pipes. Download PDF
    2011-03-24 LM Jean Leray, Nantes, France
  32. M. Ersoy, A Finite Volume Kinetic (FVK) framework for unsteady mixed flows in non uniform closed water pipes. Download PDF
    2011-03-10 Workshop Euskadi - Kyushu 2011, BCAM-Basque Center for Applied Mathematics, Derio, Basque Country, Spain
  33. M. Ersoy, A model for unsteady mixed flows in non uniform closed water pipes and a well-balanced finite volume scheme
    2011-02-24 IMATH, Toulon, France
  34. M. Ersoy, A model for unsteady mixed flows in non uniform closed water pipes and a well-balanced finite volume scheme Download PDF
    2011-02-10 LMB, Besançon, France
  35. M. Ersoy, Existence and stability results for some compressible primitive equations Download PDF
    2011-02-03 LJK, Grenoble, France
  36. M. Ersoy, A short introduction to FreeFem++ Download PDF
    2010-11-12 BCAM-Basque Center for Applied Mathematics, Derio, Basque Country, Spain
  37. M. Ersoy, Numerical dispersion and Linearized Saint-Venant Equations Download PDF
    2010-11-11 BCAM-Basque Center for Applied Mathematics, Derio, Basque Country, Spain
  38. M. Ersoy, Modeling, mathematical and numerical analysis of some compressible or incompressible flows in thin layer Download PDF
    2010-10-15 BCAM-Basque Center for Applied Mathematics, Derio, Basque Country, Spain
  39. M. Ersoy, Modélisation, analyse mathématique et numérique de divers écoulements compressibles ou incompressibles en couche mince. Download PDF
    2010-09-10 PHD, LAMA--Savoie, France
  40. M. Ersoy, Formal derivation of Saint-Venant-Exner-like model: Vertically averaged Vlasov-Navier-Stokes equations Download PDF
    2010-03-17 J. DYNAMO Rennes-France, 17-19 March, 2010.
  41. M. Ersoy, Unsteady mixed flows in closed water pipes. A well-balanced finite volume scheme Download PDF
    2010-02-02 2nd Workshop Mathematics and Oceanography Montpellier-France, 1--3 february 2010
  42. C. Bourdarias, M. Ersoy & S. Gerbi Mixed flows in closed water pipes: A kinetic approach Download PDF
    2010-01-02 French-Chinese Summer Research Institute Project “Stress tensor effects on compressible flows”, Morningside Center of Mathematics of the Chinese Academy of Sciences Beijing, 2-23 janvier 2010.
  43. M. Ersoy, A kinetic scheme for transient mixed flows in non uniform closed pipes: a global manner to upwind all the source terms Download PDF
    2009-09-07 Numerical approximations of hyperbolic systems with source terms and applications September 7 - 11, 2009 Centro Internacional de Encuentros Matemáticos Castro-Urdiales, Cantabria, Spain
  44. M. Ersoy, A kinetic scheme for transient mixed flows in non uniform closed pipes: a global manner to upwind all the source terms
    2009-07-03 LAMA--Savoie, France
  45. C. Bourdarias, M. Ersoy & S. Gerbi Air entrainment in transient flows in closed water pipes A two-layer approach. Download PDF
    2009-06-22 Modelling 2009 June 22 - 26, 2009 Roznov pod Radhostem Czech Republic
  46. M. Ersoy, A kinetic scheme for pressurized flows in non uniform pipes Download PDF
    2008-05-18 WORKSHOP "Maths & Water" Zaragoza, Spain, May 19-21, 2008



Simulations

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News and Events


  • • Scientific days of the University of Toulon, April 27, 2022

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    As part of the scientific days of the University of Toulon, April 27, 2022, at the Palais des Congrès, IMATH organizes a thematic session "Modeling in hydrodynamics".
    The purpose of this half-day session is to present new advances in terms of mathematical and numerical modeling in the field of hydrodynamics and more particularly that of the coastline. Applications may concern sedimentary movements, coastline recession, wave propagation, floating structures or flooding. Some of these problems are environmental and societal issues and are of an urgent nature. Research must take up these challenges in a multidisciplinary approach in which mathematics plays an important role to provide answers to the expectations of society around these problems which are accelerating due to climate change. For many years, the Institut de Mathématique de Toulon has participated in the development of new models allowing coupled simulations with reasonable computation times. This half-day will also be a place of exchange to discuss recent developments, in terms of physical or numerical models, coupling of models, and even new technologies that will enrich our approaches such as deep learning.
    More information here .

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Teaching


Quelques docs et tuto

•Matlab/OctavePDF.
•Script Matlab pour generer des noms de variable dans une boucle for M-FILE.

•Template Latex 0 ;-)ZIP.
•Template Latex 1 ;-) ZIP.
•Template Latex 2 ;-) ZIP.
•Exemple documents latex contenant : page de garde, figures, biblio (bibtex)ZIP.
•Exemple de présentation beamer (latex) + quelques formules ZIP.

•Script bash pour convertir par lot des images EPS au format PNG SH.

•Tuto installation CYGWIN (WINDOBS) PDF.
•Tuto Fortran MAC DL.
•Tuto OpenMP et MPI ZIP.

• Subroutine en fortran 77 pour un affichage dynamique par gnuplot ZIP

Enoncés de TD/TP


•Calcul Matriciel Numérique 1A SeaTech : TP2&3 ZIP.

•Calcul Matriciel Numérique 1A SeaTech : TP4 ZIP.

•Calcul Matriciel Numérique 1A SeaTech : TP5 ZIP.

•Calcul Matriciel Numérique 1A SeaTech : TP6 ZIP.

•Calcul Matriciel Numérique 1A SeaTech : TP7 ZIP.


•TP1 AN SEATECHZIP.

•TP2 AN SEATECHZIP.

•TP3 AN SEATECHZIP.

•TP4 AN SEATECHZIP.

•TP5 AN SEATECHZIP.

Notes de cours

•Slides Fortran 77 PDF.

•Slides Freefem++ PDF.

•Notes Optimisation PDF.

•Notes Eq. différentielles PDF.

•Formules de Taylor (Notes)PDF.

Salle de classe Virtuelle

Pour toutes questions, n'hésitez pas à me contacter par mail afin de planifier une visio depuis ma salle de classe virtuelle par BBB ou par Zoom

A question ? A remark ?

Student's simulations

(Quelques simulations numériques réalisées par des étudiants de SeaTech)


Contact

Contact


SeaTech - Ecole d'Ingénieurs de l'Université de Toulon UTLN
IMATH - Institut de Mathématiques de Toulon
avenue de l'université BP 20132,
Building M129,
83957 La Garde Cedex

+33 483 166 665

+33 672 533 633

+33 494 142 448

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