"Computational Fluid Mechanics" Option

  Syllabus - 27/09/1998

1) THEORETICAL COURSES (82h)      8 ECTS

2) NUMERICAL METHODS (112h)    11  ECTS

3) INDUSTRIAL CODES (81h)   4 ECTS

4) HANDS-ON COURSES (72 h)    6  ECTS

5) GENERAL COURSES (50h)    5  ECTS

6) FOREIGN LANGUAGES AND SPORT (80h)    4  ECTS

 

Total : 477 h / 38 ECTS

 

 


1) THEORETICAL COURSES


ADVANCED FLUID MECHANICS AND INTRODUCTION TO TURBULENCE (20h)

Semester: 1      Lectures: 20h      Hands-on:      ECTS units: 2

Keywords: Fluid mechanics, instability, turbulence, stochastic tools

Bibliography: [1] Dynamique des fluides. I.E.RHYMING, Presses Polytechniques Romandes, 1985 . Mecanique des fluides: Elements d'un premier parcours [2] P.CHASSAING, Cepadues-Editions, 1997 [3] Stochastic tools in turbulence. J.LUMLEY, Academic Press Vol12, 1970 . Physical fluid dynamics. D.J.TRITTON, Van Nostrand Reinhold Comp., 1977

Objectives:To group and give physical and mathematical knowledge needed for mastering the statistical approach of incompressible turbulence.

Program: Physical properties of the solutions of Navier-Stokes equations: Advection, diffusion, dissipation, instability and transition.Diffusion by continuous motion: turbulent mixing, vortex stretching, wall transfer. Examples of turbulent motions. Stochastic tools :correlation, spectrum. One point characteristic function transport equation: application to mean and second order moments.

M. P. CHASSAING


PHYSICS OF INCOMPRESSIBLE TURBULENCE (20h)

Semester: 1      Lectures: 20 h      Hands-on:      ECTS units: 2

Keywords: Turbulent structure, coherent motion, energy transfer, homogeneous turbulence, correlation, spectrum.

Bibliography: [1] A first course in Turbulence. H.TENNEKES & J.L.LUMLEY, The MIT Press,1972. [2] Statistical Fluid Mechanics, A.S.MONIN & A.M.YAGLOM, The MIT Press, Vol.2, 1975 [3] Turbulence: An introduction to its mechanism and theory. J.O.HINZE, Mc Graw-Hill Book Comp.,1959.

Objectives:To get a phenomenological insight on eddy structures to achieve the understanding of energy transfer in incompressible turbulence.

Program: Vorticity dynamics: vorticity equation, 2D AND 3D interaction modes. Enstrophy. Coherent structures: origin, pairing. Homogeneous and isotropic turbulence: correlations and spectra dynamics. The Loitsyanski invariant, the Lin's equation, the Batchelor expression of the dissipation, the Kolmogorov assumptions and their consequences: energy cascade et -5/3 spectrum.

M. P. CHASSAING


GREAT REYNOLDS NUMBER TURBULENCE MODELLING (20h)

Semester: 1      Lectures: 20 h      Hands-on:      ECTS units: 2

Keywords: Turbulence modelling, single point closure, free shear flows

Bibliography: [1] The structure of turbulent shear flow. A.A.TOWNSEND, 2nd Ed., Cambridge Univ. Press, 1976. [2] Turbulence models and their applications. B.E.LAUNDER, W.C.REYNOLDS, W.RODI, J.MATHIEU, D.JEANDEL Ed. Eyrolles, 1984. [3] Modelisation et simulation des ecoulemenst turbulents. R.SCHIESTEL, Hermes, 1993.

Objectives: Knowledge of single point closures to get the skills to decide on the suitable model to predict high Reynolds number turbulent flows.

Program: Classification of turbulent flows. Homogeneous turbulence, turbulent shear flows.Basic mecanisms: isotropic relaxation, mean motion effects (contraction, shear,pure deformation,rotation),pressure- redistribution, diffusion, dissipation. Overview of currents methods (Direct numerical simulation, Large eddy simulation, spectral and single point closures). First and second order models based on linear and non linear closure schemes.

M. P. CHASSAING


HYDRODYNAMIC INSTABILITIES (10h)

Semester: 2      Lectures: 10 h      Hands-on:      ECTS units: 1

Keywords: dynamical system, instabilities, bifurcations, stability of flows

Bibliography: http://www.enseeiht.fr/fr/formation/hy/MFN/travaux.html

Objectives: To reinforce the understanding of the hydrodynamic flow stability. To get some basic notions of the dynamical system theory. To build a code solving a simple dynamical model.

Program: The course starts with an introduction to bifurcation theory through the detailled examination of simple dynamical systems: saddle-node bifurcation, pitchfork bifurcation and Hopf bifurcation. The study of the Lorenz model is used the introduced the calculus of the stability of equilibrium in dynamical system with several degrees of freedom. The drawing of the phase portrait of the simple pendulum enables the introduction to potential or hamiltonian conservative systems.

In the second part of the course, the explicit derivation of the critical Rayleigh number of the Rayleigh-BÈnard convection is made for the Boussineq approximation and free-slip boundary conditions. This calculation enables the introduction of the concept of the stability of equilibrium in hydrodynamic flows.

M. O. THUAL


TRANSPORT PHENOMENA IN SOILS (12h)

Semester: 1     Lectures: 12h      Hands-on:      ECTS units: 1

The objective of this course is the analysis and the modelling of the main mechanisms controlling the migration and fate of pollutants in soils and subsoils. The main techniques of soil remediation are also described. The main topics that are covered are: diffusion in porous media, dispersion in porous media, sorption phenomena, multiphase flow in porous media, water flow modelling in the unsaturated zone (Richards equation), transport phenomena with phase change in porous media (application to soil venting). The numerical problems associated with the various models presented are systematically discussed.

M.M. PRAT


2) NUMERICAL METHODS


ANALYSIS OF NUMERICAL SCHEMES FOR PARTIAL DIFFERENTIAL EQUATIONS [I] (20h)

Semester: 1      Lectures: 20h      Hands-on:      ECTS units: 2

Objective: Introduce the basic techniques used to dicretize linear partial differential equations and to analyse convergence and precision of finite difference schemes for initial value problems

Key words: numerical analysis, pde, discretization techniques

References: [1] J. W. THOMAS, Numerical Partial Difference Equations, Springer-Verlag, 1995. [2] C. HIRSCH, Numerical Computation of Internal and External Flows (Vol. 1), John Wiley, 1988. [3] C. A. J. FLETCHER, Computational Techniques for Fluid Dynamics, Springer-Verlag, 1991

Program: Classical discretisation techniques for differential operators are introduced within the general framework of the weighted residual method. Some details are given for finite difference, finite volume, finite elements and spectral methods. Convergence proof based on Lax equivalence theorem and spectral analysis are developped for finite difference discretizations of linear initial value problems. These tools are used to choose suitable schemes for several typical partial differential equations.

M. D. ASTRUC


NUMERICAL METHODS FOR COMPRESSIBLE FLOWS COMPUTATIONS [II] (20h)

Semester: 1      Lectures: 20h      Hands-on:      ECTS units: 2

Objective: Introduction to the state-of-the -art numerical techniques used to compute compressible flows and other quasi-linear hyperbolic problems

Key words: compressible flows, numerical schemes, Riemann solvers, open boundary conditions

References: [1] J.-L. ESTIVALEZES, Systèmes de lois de conservation hyperboliques, théorie et approximation, Polycopié ENSEEIHT, 1998. [2]C. HIRSCH, Numerical Computation of Internal and External Flows (Vol. 2), John Wiley, 1988.

Program: Hyperbolicity and related concepts are discussed in the perspective of numerical computation. Classical techniques based either on a combined space-time discretization (Lax-Wendroff like) schemes or on the method of line are introduced. Then shock capturing schemes based on Riemann solvers are discussed as well as high order schemes. Practical implementation of boundary condition is discussed with emphasis on open boundary conditions.

M. D. ASTRUC, J.-L. ESTIVALEZES


NUMERICAL METHODS [III] (20h)

Semester: 2     Lectures: 20 h      Hands-on:      ECTS units: 2

M. J. MAGNAUDET


COMPUTATION METHODS FOR COMPLEX FLOWS [IV] (20h)

Semester: 1      Lectures: 20 h      Hands-on:      ECTS units: 2

Keywords: incompressible flow, combustion flow, boundary layer, mesh.

Objectives: Introduce methods for incompressible viscous flows and combustion flows.

Program: The course starts with an introduction to the computational grid methods to obtain a mesh for a given domain. Methods for the boundary layer in the wall region are develloped. Specific methods for incompressible flow and a topic on combustion flow are also introduced.

M. D. DARTUS


NUMERICAL ALGORITHM FOR LINEAR ALGEBRA (20h)

Semester: 1      Lectures: 20 h      Hands-on:      ECTS units: 2

Bibliography: [1] Anderson, E., Bai, Z., Bischof, C., Demmel, J.W., Dongarra, J.J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., and Sorensen, D.C. (1992), LAPACK Users' Guide. SIAM, Philadelphia. [2] J. J. Dongarra and I. S. Duff and D. C. Sorensen and H. A. van der Vorst (1991). Solving Linear Systems on Vector and Shared Memory Computers, SIAM, Philadelphia. [3] Duff, I.~S. (1996), Sparse numerical linear algebra: direct methods and preconditioning, Technical Report RAL 96-047, Rutherford Appleton Laboratory.

Objectives: Our goal is to introduce some basic notions and to describe the main direct solution techniques used in linear algebra. We also describe their implementation on high-performance computers.

Program: We first describe some fundamental concepts: finite precision arithmetic, error, sensitivity, condition number, \ldots. Then, we consider the solution of dense linear systems and we show how crucial is the use of numerical libraries (such as the BLAS and LAPACK) for developing portable and efficient numerical software on high-performance serial and parallel computers (including networks of computers). Finally, we consider the solution of large and sparse systems of linear equations using direct methods. Hands-on sessions will illustrate some of the code performance and implementation aspects.

M. P. AMESTOY, Ph. BERGER, M. DAYDE


DISTRIBUTED PARALLEL COMPUTING (12h)

Semester: 1      Lectures: 4 h      Hands-on:  8 h    ECTS units: 1

M. P. AMESTOY


3) INDUSTRIAL CODES


CONCEPTION OF INDUSTRIAL CODE SERIES (20h)

Semester: 1      Lectures: 20h      Hands-on:     ECTS units:

Program: In the first part of this course we learn how to add small extension to differents industrial code series. In a second part methods are given to evaluate quality of a solution given by a code. Last part is center around devellopement of industrial code series using classical methods of "genie logiciel".

M. D. DARTUS


APPLIED INFORMATICS(10h)

Semester: 1      Lectures: 10h      Hands-on:     ECTS units:

M. D. ASTRUC


NEW CODES WORKSHOP (51h)

Semester: 1 and 2      Lectures:      Hands-on: 51h      ECTS units: 4

Keywords: computation codes, industrial codes, computational modelling

Bibliography: http://www.enseeiht.fr/fr/formation/hy/MFN/travaux.html

Objectives: To get a know-how in the installation, exploration and mastering of industrial codes and their software environment. To become familiar to the use of the codes installed on the intranet server.

Program: During this hands-on workshop the approach of the industrial codes which are resident on the Intranet server is reached through three actions: installation, exploration and maintenance. The installation of new code increase the number of available softwares on the server. The exploration of the installed codes is achieved through the treatment of physical cases both realistic or idealized. At last, the maintenance of the software environment of these codes increased the user friendship (writing of manuals, on-line helps, ...). The workshop is divided into three sessions of about five weeks each. During one session, a two people team achieved a well defined task. Each task produces a manual and a report which goal is to ease the future use of the installed codes.

The following codes have been installed or explored during previous sessions: FLUENT, PHOENICS, TELEMAC-2D, ARTEMIS, FLUIDYN-NS, PANACHE, BIGFLOW, LIDO, TSAR, MOBILY, TRACER, CLAWPACK, LATEX, XPVM, REF-DIF, ESTET-ASTRID, etc.

M. O. THUAL, M. D. DARTUS, M. PH. SCHMITZ


4) HANDS-ON COURSES


NUMERICAL SCHEMES AND BOUNDARY CONDITIONS HANDS-ON (24h)

Semester: 1      Lectures:      Hands-on: 24h     ECTS units: 2

Keywords: Euler, Acoustics, Numerical Schemes, Boundary Conditions, Characteristic waves, Stability

Bibliography: "Numerical Computation of Internal and External FLows", C. Hirsch, John Wiley & Sons, 1988

Objectives: This course is aimed to show to the students the behavior of numerical schemes, on the example of the compressible monodimensional Euler equations. It is then a good opprtunity to study some aspects of physical acoustics.

Program: All calculations are performed with the code SLC, of which a quasi-complete version is given to limit the programming time during the course. Only a few lines are to be completed, so that the student gets familiar with the code and generally speaking with the programming technique in computational fluid dynamics. When needed, the theory is recalled in class. We start with the analytical and numerical study of the behavior and stability of different numerical schemes. Then we focus on the boundary conditions implementation, first in simplified configurations then in more complex physical situations. The student is encouraged to freely use the code to perform other types of simulations.

B.CUENOT, F.NICOUD


GENERAL PURPOSES FLUID MECHANICS CODES HANDS-ON (24 h)

Semester: 1      Lectures:      Hands-on: 24 h    ECTS units: 2  

Program: In this course the numerical code PHOENICS (CHAM/TRANSOFT) is used to study a layer of fluid between horizontal parallels walls maintained at different temperatures (Free convection, Rayleigh-Benard instability). After having define the problem to be solved (choise of the equations, of the models, of the boundary conditions and of the initial conditions), we determine the critical Rayleigh number above which stationnary convective rolls appear. We analyse the dynamical and thermal behavior of the convective structures at the onset of motion. Numerical results are compared to theoretical results obtained from linear stability analysis.

M. V. ROIG, M. D. DARTUS


FREE SURFACE FLOW HANDS-ON (24h)

Semester: 1      Lectures:      Hands-on: 24 h   ECTS units: 2   (optional 1)

Objective: Gain a practical experience with free surface flow industy-standard numerical computation code. Apply the concepts of numerical analysis to an industy-standard software.

Key words: free surface flows, numerical computation, industry-standard code

References: TELEMAC system user's manuals.

Program: The aim of this course is to study free surface flows using TELEMAC-2D (EDF-DER-LNH). This code solves Saint-Venant equations which are non linear hyperbolic partial differential equations. The principal objective is to test different schemes to solve an accademical problem, for instance the wave resulting from the failure of a dam. Numerical results are compared with analytical solution to analyse sensibility to different numerical parameters such as time and space steps and to test several linear system resolution methods available in this code.

MM. M. M. MAUBOURGUET, D. ASTRUC


AERODYNAMICS AND PARALLEL COMPUTING HANDS-ON (24h)

Semester: 1      Lectures:      Hands-on: 24 h    ECTS units: 2 (optional 2)

Objective: This H.O.C. aims to familiarize the students with the handling of a parallel solver of computational fluid mechanics (CFD) in the frame of a complete computation cycle: mesh generation, internal and external flow calculations, visualization and interpretation of results.

Key words: Numerical simulation, computations in aerodynamics, parallel computing, mesh generation, unstructured methods.

References: T. Schoenfeld and M.A. Rudgyard, "A Cell-Vertex Approach to Local Mesh Refinement for the 3-D Euler Equations", AIAA paper 94-0318. J.-D. Mueller, T. Schoenfeld and M.A. Rudgyard, "A Comparison of the Treatment of Hanging Nodes for Hybrid Grid Refinement", AIAA paper 97-1859.

Background required: "Simulation des Écoulements Compressibles" course of Astruc and Estivalèzes, basic knowledges in parallel computing.

Program: This course is based on the parallel flow solver AVBP developed at CERFACS, which solves the compressible three-dimensional Navier-Stokes equations on unstructured grids. In the first part a brief introduction to the code and the pre- and postprocessing tools is given and calculations of well-documented standard test cases are undertaken. The second part of the course is devoted to a little project which is defined by the students. This project comprises aspects such as mesh generation, setting up of boundary conditions, interpretation of results, etc. and the students learn to adjust the various run parameters in order to achieve correct solutions.

M. T. SCHOENFELD, M. F. DUCROS


6) GENERAL COURSES


INDUSTRIAL PROJECTS ON  ENVIRONMENT (40h)

Semester: 2      Lectures:      Hands-on: 40 h      ECTS units: 5 (optional 1)

Keywords: environment, hydraulics, student projects

Bibliography: http://www.enseeiht.fr/fr/formation/hy/MFN/travaux.html

Objectives: To realise an ambitious project close to the real engineer work. To use a wide scope of knowlege for an concrete project. To be part of a team work.

Program: The choice and the definition of the project is left to the initiave groups of two persons gathered in team of about ten, in the framework of well defined constraints concerning scientific domains and organisational aspects. For instance, the two-people group projects must find integration in the ten-people team subject. Each team has to choose and received an invited speaker for a seminar and an expertise of the team project. The presentation of the two-people groups and team work is made through a multimedia support with hypertext file (Intranet) in order to enhance the group interactions during the course. The final presentation of the course projects is made in front of a large public.

During previous sessions of this course, the following projects have been realized: Study of Bayonne and its coast - Implementation of a damn - Protection against flood in Agen - Study of the Arcachon bassin - Restoring the marine aspect of Mont Saint Michel - The ecological harbour of Noirmoutiers - Interaction between the Tarn and Garonne rivers with the Malause bassin - La Reunion - The Saint-Malo bay, etc.

M. O. THUAL, M. D. ASTRUC


INDUSTRIAL PROJECTS ON  COMBUSTION (40h)

Semester: 2      Lectures:      Hands-on: 40 h     ECTS units: 5 (optional 2)

Keywords: combustion

Objectives: To realise an ambitious project close to the real engineer work.

MM. Th. POINSOT, R. BAZILE


INDUSTRIAL PROJECTS ON  CHEMICAL ENGINEERING (40h)

Semester: 2      Lectures:      Hands-on: 40 h     ECTS units: 5 (optional 3)

Keywords: fluid mechanics, chemical engineering.

Objectives: To realise an ambitious project close to the real engineer work.

MM. O. SIMONIN, V. ROIG


SEMINARS (6h)

Semester: 1 & 2     Lectures:   6 h   


COMMUNICATION TECHNIQUES (4h)

Semester: 1 & 2     Lectures:   4 h   


7) FOREIGN LANGUAGES AND SPORT


ENGLISH (40h)

Semester: 1 & 2     Lectures:   40 h   

GERMAN (40h)

Semester: 1 & 2     Lectures:   40 h   

OPTIONAL FOREIGN LANGUAGES (40h)

Semester: 1 & 2     Lectures:   40 h   

German, Spanish, Italian, Russian, Japones, Arabic.

SPORT ACTIVITIES (40h)

Semester: 1 & 2     Training :   40 h   


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