Driss Yakoubi, Ph.D




   
   

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    I am a postdoc fellow at GIREF (since September 2010), in the Department of Mathematics and Statistic of University Laval, Quebec city. My research works within the GIREF concerns the resolution of the Navier Stokes equations by finite element method and the numerical identification of the critical Reynolds number who indicates the asymmetry phenomena for fluid flow. This work is under the supervion of M. A. Fortin.

    During my Postdoc within the team REO of the INRIA- Paris-Rocquencourt (Sept.2008-Sept2010), my research work can be divided into two parts. The first one concerns the modelling of the flows of the air in the respiratory system and to determine effective algorithms relative to the model. The second part concerns the study of the influence of a spray evolving in the air, in the respiration framework.
    This work is under the supervion of Mme. C. Grandmont.

    I did my PhD at Jacques-Louis Lions Laboratory of Paris VI University during 2003 to 2007, entitled "Analyse et mise en oeuvre de nouveaux algorithmes en méthode spectrales " under the supervision of: Christine Bernardi and Stéphane Del Pino.
    The work done in the preparation of my thesis can be divided into three parts. The first one concerns the study of a model for the interaction of turbulent fluids (the water of the ocean and the atmosphere above it). The second part is about the use spectral methods to discretize elliptic boundary value problems in non-tensorial domains. The last part concerns the extension of an existing object-oriented finite element code to incorporate also spectral methods, its validation and the application to the numerical solution of the ocean- atmosphere problem considered in the first part.

      Research


      My work is focused on the:

    • Mathematical and numerical analysis of PDEs,
    • Finite Element approximation, Spectral Methods,
    • Computational Fluid Dynamic (CFD) ,
    • Laminar Instability and Flow Bifurcations ,
    • Fluid Structure Interaction,
    • Turbulence Model (RANS Model),
    • Modelling of the Air Flow in the Respiratory Tract,
    • Bio-Mathematical Modelling,
    • Scientific Computing.

      • Publications



    • 12. Spectral discretization of Darcy's equations coupled with the heat equation. With C. Bernardi and S. Maarouf. Submited Preprint
    • 11. Spectral discretization of a model for organic pollution in waters. With C. Bernardi. Submited Preprint
    • 10. Finite element discretization of the Stokes and Navier-Stokes equations with boundary condition on the pressure. With C. Bernardi and T. Chacon Rebollo.
      Minor revision in SIAM Journal on Numerical Analysis Preprint
    • 9. Spectral discretization of an unsteady flow through a porous solid. With C. Bernardi and S. Maarouf. Submited Preprint
    • 8. 3D Model for Coupled Turbulent Fluids: Numerical Analysis of Finite Element Approximation. With T. Chacon Rebollo. Submited Preprint
    • 7. A Coupled prediction scheme for solving the Navier-Stokes and convection-diffusion equations. With J. Deteix and A. Jendoubi. SIAM Journal on Numerical Analysis 2014 52:5, 2415-2439: Preprint
    • 6. An immersed boundary method for fluid flows around rigid objects. With A. Jendoubi, A. Fortin and C. Tibirna. Int. J. Numer. Meth.Fluids. doi: 10.1002/fld.3884: Preprint
    • 5. Numerical Method for the 2D Simulation of the Respiration. With A. Devys, C. Grandmont, B. Grec and B. Maury. Esaim. Proc. 30 (2010) 153-165: Preprint
    • 4. Influence Of The Spray Retroaction On The Airflow. With L. Boudin, C. Grandmont and B. Grec. Esaim. Proc. 28 (2009) 162-181: Preprint
    • 3. An Iterative Procedure to Solve a Coupled Two-Fluids Turbulence Model. With T. Chacon Rebollo and S. Del Pino. M2AN 44 (2010) 693-713: Preprint
    • 2. Une borne inférieure pour la constante de la condition inf-sup sur l'opérateur de divergence. With S. Del Pino and U. Razafison. C. R. Math. Acad. SCi. Paris 346 (2008): Preprint
    • 1. Analyse et mise en oeuvre de nouveaux algorithmes en méthode spectrales. Ph.D Thesis(2007), University Paris VI.Preprint

      • In Preparation



    • Numerical treatment of dissipative boundary conditions for the Navier-Stokes equations. Application to the respiratory tract. With A. Devys and C. Grandmont.
    • A coupled approach of the projection method applied to free boundary problem in fluid. With J. Deteix and A. Jendoubi.
    • 3D Model for Coupled Turbulent Fluids : Numerical Analysis of Spectral Method Approximation.

      • Some Conferences


    • Ph.D Thesis: Defense Presentation: [PDF] (French)


    • A Finite Element Approximation of a Coupled Model for Two Turbulent Fluids [PDF]
      Fifth FreeFem workshop on Generic Solvers for PDEs : FreeFem++ and its Applications, 10-12 December 2013, Paris. France.
    • A hierarchical iterative solver and Fractional timestepping schemes for the Navier-Stokes equations [PDF]
      Canadian Mathematical Society Winter Metting, CSM 2012 7-10 December 2012, Montreal. Canada.
    • A hierarchical iterative solver for the Navier-Stokes equations. [PDF]
      Canadian Applied and Industrial Mathematics Annual Meeting, CAIMS 2012. 24 - 28 Juin 2012, Toronto.
    • An Iterative Procedure to Solve a Coupled Two-Fluids Turbulence Model. [PDF]
      Seminar of Numerical Analysis. October 8th 2010. Laval University, Quebec City.
    • Numerical Modelling of the Air Flow in the Respiratory Tract. [PDF]
      International Congress In Mathematical Fluid Dynamic And Its Applications. June 21th - 24th 2010. Rennes, France. >
    • Numerical Modelling of the Air Flow in the Respiratory Tract. [PDF]
      Seminar of Numerical Analysis. University of Sevilla, Spain. February 17th 2010.
    • Numerical Modelling of the Air Flow in the Respiratory Tract. [PDF]
      Seminar of Numerical Analysis. University Paris V, France. April 10th 2009.
    • A Fictitious Domain Like Spectral Method in Complex Geometries. [PDF]
      Seminar of Mathematics. University of Annaba, Algeria. October 2007.
    • An Iterative Procedure to Solve a Coupled Two-Fluids Turbulence Model.[PDF]
      ICIAM 6th International Congress on Industrial and Applied Mathematics. Zurich, Suisse. 16-20 Juillet, 2007.
    • Spectral Method in FreeFEM3D Software. Journee Interne of Jacques-Louis Lions Laboratory. Paris, France. June 25th 2007.
    • An Iterative Procedure to Solve a Coupled Two-Fluids Turbulence Model : Unicity of Solution and Convergence of the Scheme.[PDF]
      38th French National Congress on Numerical Analysis. Guidel, Morbihan, France. May 29th to June 2nd 2006.
    • Convergence of a Iteratif Scheme of the Fluid Turbulence Model : Unicity of Solution and Convergence of the Scheme.
      8th Moroccan National Congress on Numerical Analysis and Optimization. Rabat, Morocco. December 14th - 16th 2005.
    • Some Results on the Convergence of an Iterative Procedure of a Turbulent Fluids Model.
      2nd French National Congress on Industrial and Applied Mathematics (SMAI). Evian, France. May 23th - 27th 2005.

      • Teaching


    • Teaching at University Laval 2011-2012: 45h X 2
    • Teaching at University Paris VI 2006-2008: 96 X 2
    • Teaching Assistant at the National School of Computer Science for Industry and Business ENSIIE : 45h
    • Teaching Assistant at the University Paris XI-(Orsay) 1997-2000 at Faculty Jean Monnet: 200 h