**"Computational Fluid Mechanics" Option**

Syllabus - 27/09/1998

1) THEORETICAL COURSES (82h) **
8 ECTS**

- ADVANCED FLUID MECHANICS AND INTRODUCTION TO TURBULENCE
(20h) 2
*ECTS* - PHYSICS OF INCOMPRESSIBLE TURBULENCE (20h) 2
*ECTS* - GREAT REYNOLDS NUMBER TURBULENCE MODELLING (20h) 2
*ECTS* - HYDRODYNAMIC INSTABILITIES (10h) 1
*ECTS* - TRANSPORT PHENOMENA IN SOILS (12h) 1
*ECTS*

2) NUMERICAL METHODS (112h) ** 11
ECTS**

- ANALYSIS OF NUMERICAL SCHEMES FOR PARTIAL DIFFERENTIAL
EQUATIONS [I] (20h) 2
*ECTS* - NUMERICAL METHODS FOR COMPRESSIBLE FLOWS COMPUTATIONS
[II] (20h) 2
*ECTS* - NUMERICAL METHODS [III] (20h) 2
*ECTS* - COMPUTATION METHODS FOR COMPLEX FLOWS [IV] (20h) 2
*ECTS* - NUMERICAL ALGORITHM FOR LINEAR ALGEBRA (20h) 2
*ECTS* - DISTRIBUTED PARALLEL COMPUTING (12h) 1
*ECTS*

3) INDUSTRIAL CODES (81h) ** 4 ECTS**

- CONCEPTION OF INDUSTRIAL CODE SERIES (20h)
- APPLIED INFORMATICS (10h)
- NEW CODES WORKSHOP (51h) 4
*ECTS*

4) HANDS-ON COURSES (72 h) ** 6
ECTS**

- NUMERICAL SCHEMES AND BOUNDARY CONDITIONS HANDS-ON (24h)
2
*ECTS* - GENERAL PURPOSES FLUID MECHANICS CODES HANDS-ON (24 h)
2
*ECTS* - FREE SURFACE FLOW HANDS-ON (24h) 2
*ECTS (optional 1)* - AERODYNAMICS AND PARALLEL COMPUTING HANDS-ON (24h) 2
*ECTS (optional 2)*

5) GENERAL COURSES (50h) ** 5 ECTS**

- INDUSTRIAL PROJECTS (40h) 5
*ECTS* - SEMINARS (6h)
- COMMUNICATION TECHNIQUES (4h)

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

**Total : 477 h / 38 ECTS**

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 *

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 *

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 *

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 *

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 *

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*

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*

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*

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*

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

*M. P. AMESTOY*

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*

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

*M. D. ASTRUC*

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 *

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 *

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*

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*

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*

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 *

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*

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*

Semester: 1 & 2 Lectures: 6
h

Semester: 1 & 2 Lectures: 4
h

Semester: 1 & 2 Lectures: 40 h

Semester: 1 & 2 Lectures: 40 h

Semester: 1 & 2 Lectures: 40 h

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

Semester: 1 & 2 Training : 40 h

Webmaster : thual@imft.fr