Fluid Mechanics: Fundamentals and Applications (MF2A)

Plannings     M1     M2 Fluid Mech.     M2 MSH     M2 AA

First Semester (30 ECTS)

Second semester (30 ECTS)

The Modeling and Simulation in Hydrodynamics (MSH) program provides advanced training in fields related to hydrodynamics. It provides students with the theoretical and digital tools needed to study and understand simple or complex fluid flows. Topics covered include homogeneous and two-phase fluid flows, suspensions and porous media, turbulent flows and flows in natural environments.

The originality of the course lies in its balanced approach to physical and theoretical modeling on the one hand, and numerical modeling and simulation on the other.

The opportunities are vast and range from healthcare and transport to the oil industry and the environment.

Organization of the year

The course comprises one semester of teaching from September to February, in the form of two eight-week periods, each punctuated by an examination session. The list of teaching units (UE) is outlined below. The second semester, starting in March, is dedicated to a 20-week internship.

In recent years, students have been able to complete their internships in industry (Institut Français du Pétrole, Saint-Gobain, Renault, BMW, EDF), research organizations (CEA, ONERA) or within the academic world in laboratories linked to Sorbonne University (Institut Jean le Rond d'Alembert, LOCEAN, LIMSI, FAST, PMMH) or elsewhere in France and abroad.

Applications

September 2023: The semester will begin with a four-day course to prepare students for the mathematical techniques and computer facilities required for the curriculum.

Program

First period (September to November)

• Mechanics of continuous fluid media, 3 ECTS (C. Croizet, SU code MU5MEF00)
• Multiphase flows, 1ère part, 6 ECTS (E. Sultan, D. Fuster, SU code MU5MEF02)
• Turbulence dynamics, 3 ECTS (P. Cinnella, SU code MU5MEF03)
• Numerical methods for incompressible flows, 3 ECTS (B. Podvin, SU code MU5MEF04)
• Practical digital simulation, 3 ECTS (F. Picella, R. Pennel, SU code MU5MEF32)

Second period (December to February)

• Porous media and suspensions, 3 ECTS (A. Mongruel and D. Baltean-Carlès, SU code MU5MEF23)
• Flow and transfer in natural environments, 3 ECTS (S. Mergui, P.-Y. Lagrée, SU code MU5MEF05)
• Multiphase flows, 2ème part.

+ 2 optional units can be chosen from other courses, 3 ECTS, such as (non-exhaustive list):

• Turbulence models (course in English), 3 ECTS (P. Cinnella, location: Sorbonne University, SU code MU5MEF01)
• Flow instabilities, 3 ECTS (J.-C. Robinet, location: ENSAM, SU code MU5MEF12)
• Vortex dynamics (course in English), 3 ECTS (I. Delbende, SUcode MU5MEF06)
• Nonlinear dynamics and chaos, 3 ECTS (J.-C. Loiseau, location: ENSAM, SU code MU5MEF14)

3e period (from March)

• Internship (minimum 20 weeks), 27 ECTS
• English, 3 ECTS.

 
Registrations

Deadline

If you live abroad, please consult https://www.campusfrance.org/ . For some countries, the deadline for applying to the "CEF-Etudes en France" procedure is very early in the year: applications open in December and the deadline varies from country to country (sometimes early March or even earlier).

Registration form

Applications open in April for the 2023-24 academic year. Once applications have opened, go to the dedicated website and select "M2 Mécanique : Mécanique des fluides Fondements Applications" and follow the procedure. Do not forget the "Complementary forms" tab, where you can specify your choice or preferences between Fluid Mechanics courses (MSH, AA, FM). If you live in one of the countries covered by the "CEF-Etudes en France" procedure, you must apply directly through Campus-France. Registration fees at Sorbonne University are minimal.

The Aerodynamics and Aeroacoustics (AA) program provides advanced training in the fields of aerodynamics, aeroacoustics and fluid-structure interaction. The courses offered in this program provide students with the knowledge required for fundamental and applied research activities in these fields. Emphasis is placed on physical and theoretical modeling and the associated digital simulation methods.

There are numerous industrial applications and outlets, particularly in the field of aeronautical and land transport, where reducing fuel consumption and noise pollution and improving passenger comfort are major challenges (see the Outlets section at the bottom of this page).

Organization of the year

This program is co-accredited with the École Nationale Supérieure des Arts et Métiers (ENSAM). Teaching is shared equally between Sorbonne University and ENSAM.

The course comprises one semester of teaching from September to February, in the form of two eight-week periods, each punctuated by an examination session. The list of teaching units (UE) is provided at the bottom of this page. The second semester, starting in March, is dedicated to a 20-week internship.

In recent years, students have been able to complete t their internships in industry (Safran Aircraft Engines, Airbus, SNCF), in research organizations (ONERA, IRSTEA) or within academia in the mechanics laboratory at Sorbonne University (Institut Jean le Rond d'Alembert) or elsewhere in France and abroad (LIMSI, Institut de Mécanique des Fluides de Toulouse, École de l'Air de Salon de Provence, TU Delft...).

> Applications

The start of the 2023-2024 academic year: the semester begins with a four-day course to prepare students for the mathematical techniques and computer installations required for the course.

Program

First period (September to November)

• Fundamental Aerodynamics, 3 ECTS (X. Gloerfelt, location: ENSAM, SU code MU5MEF08)
• Numerical methods for compressible flows, 3 ECTS (V. Daru and X. Merle, location: ENSAM, SU code MU5MEF09)
• Turbulence dynamics, 3 ECTS (P. Cinnella, location: Sorbonne University, SU code MU5MEF03)
• Aero-elasticity (course in English), 3 ECTS (J.-C. Chassaing and A. Vincenti, location: Sorbonne University, SU code MU5MEF10)
• Practice of numerical simulation, 3 ECTS (F. Picella, R. Pennel, location: Sorbonne University, SU code MU5MEF32)

Second period (December to February)

5 UE from the following 7

• Turbulence models (course in English), 3 ECTS (P. Cinnella, location: Sorbonne University, SU code MU5MEF01)
• Optimization in aerodynamics (course in English), 3 ECTS (A. Belme, location: Sorbonne University, SU code MU5MEF39)
• Vortex dynamics (course in English), 3 ECTS (I. Delbende, location: Sorbonne University, SU code MU5MEF06)
• Aeroacoustics, 3 ECTS (X. Gloerfelt, location: ENSAM, SU code MU5MEF11)
• Flow instabilities, 3 ECTS (J.-C. Robinet, location: ENSAM, SU code MU5MEF12)
• High-fidelity numerical simulation of turbulent flows, 3 ECTS (L. Sciacovelli, location: ENSAM, SU code MU5MEF13)
• Control theory, 3 ECTS (J.-C. Loiseau, location: ENSAM, SU code MU5MEFxx)

Third period (from March)

• Internship (minimum 20 weeks), 27 ECTS
• English, 3 ECTS

 
Registrations

Deadline

If you live abroad, please consult first https://www.campusfrance.org/ . For some countries, the deadline for applying to the "CEF-Etudes en France" procedure is very early in the year: applications open in December, and the deadline varies from country to country (sometimes early March or even earlier).

Registration form

Applications open in April for the 2022-23 academic year. Once applications have opened, go to the dedicated website and select "M2 Mécanique : Mécanique des fluides Fondements Applications" and follow the procedure. Don't forget to use the "Additional forms" tab to specify your choice or preferences between Fluid Mechanics courses (AA, MSH, FM). If you live in one of the countries covered by the "CEF-Etudes en France" procedure, you must apply directly through Campus-France. Registration fees at Sorbonne University are minimal.

Testimonials

Arnaud (class of 2014-15) - The "Fluid Mechanics" master's degree gave me the opportunity to spend a year in R&D at Airbus France/Germany, as well as an end-of-studies internship at ISAE-SUPAERO. The latter led to a PhD in aerodynamics and numerical simulations, in partnership with the French Defence Procurement Agency (DGA). I'm now working in collaboration with Hyperloop Transportation Technologies to carry out CFD studies to remove certain technological barriers to this new means of transport.

Miguel (class of 2014-15) - The Fluid Mechanics: Fundamentals and Applications course provides all the foundations needed for engineering careers in this field. I chose to specialize in aerodynamics and aeroacoustics, and the various courses have given me a solid grounding in this field. The program is well articulated and allows the assimilation of numerous theoretical notions via the realization of application projects on current issues. This master's degree opened the door to several research and industrial experiences (Airbus, Altran and Ecole Centrale de Lyon) and a CIFRE thesis with Safran Aircraft Engines, which enabled me to take up a position in R&D on turbomachinery aeroacoustics. I have no hesitation in recommending this course to anyone wishing to specialize in aerodynamics. The course provides methodical training for technical positions, whether in laboratory research or R&D in industry.

Important announcement:

Registration for this program  is closed for 2024-2025. For 2025-2026, if you reside aborad, first visit the page https://www.campusfrance.org/en .

This master program is part of the master curriculum in science and technology of Sorbonne University, jointly operated with Ecole Polytechnique, and is entirely taught in English. It is directed at students preparing for a science or engineering career in academia or industry. Most courses are given in English by prominent scholars. Courses all take place during the first semester (September to February). A research project is conducted in France or abroad, in academia or industry, during the second semester (4 to 6 months, March to early July or September). Entering students should have completed undergraduate studies in science with elementary introduction to fluid mechanics.

Modern Fluid Mechanics

Fluid mechanics describes the macroscopic motion of fluids, building from first principles of classical physics and thermodynamics. Modern fluid mechanics is a very active research area, driven by its fundamental or curiosity driven research interest as an exemplary complex systems, and by its extreme importance in natural and industrial phenomena.

For the curiosity driven, fluid mechanics offers the example of a complex system in which the basic equations are known (the Navier-Stokes equations have been known for more than a century) but the resulting behavior is hard to predict and complex. Moreover, the very proof of the existence of solutions escapes researchers leading to such tantalizing problems as those being stated by the Clay Prize.

For the application driven, fluid mechanics has long been the province of aircraft designer, "rocket scientists" or automobile designers. However the recent increase in computer power and algorithmic ingenuity, as well as advances in flow visualization, have opened the field to much more numerous applications such as biological and medical engineering, process and chemical engineering, civil engineering, ocean, nuclear or petroleum engineering. The natural science of geophysics, astrophysics and planetary sciences also heavily rely on fluid mechanics.

Application of Fluid Mechanics

Fluid phenomena are everywhere. Beyond aerodynamics, meteorology and climatology rest on the predictability of flow phenomena, either for short term weather predictions or for accurate long term modelling of global change. The automotive and petroleum industries have an ever growing need for numerical studies and for talented engineers to set up and interpret the corresponding simulations. The past ten years have seen the opening of the whole new domain of chemical, process and mining engineering to various simulation approaches.

Learning outcomes

The language of the program is English except for the optional "French for Foreigners" course. As a result the graduate will have the capacity to participate in meetings in English with researchers and engineers of international level. He will be able to read, understand and analyze a recent scientific paper in the general area of fluid mechanics, to evaluate the relevance of the various approximations needed to solve a problem, to implement the numerical modelling of a fluid phenomenon, through the resolution of the Navier-Stokes equations or more specific models, to propose and evaluated numerical resolution methods using research or commercial Computational Fluid Dynamics (CFD) or Computational Multiphase Fluid Dynamics (CMFD) codes such as Gerris, Basilisk or FreeFem.

The second year (which is recommended for most students) of the master is organized as most programs of Sorbonne University. Classes begin around september 20 with several information meetings. The first semester of the second year is organized in two eight-week periods.

Program

1st semester (from September to February)

• Current topics in fluid mechanics: Aerodynamics (V. Brion – X)  and Optimisation (T. Sayadi – CNAM)    3 ECTS code SU MU5MEF41
• Drops, Bubbles and Co (D. Quéré & C. Baroud -X)    3 ECTS    code SU    MU5MEF17
• Experimental Methods in Fluid Mechanics (R. Monchaux – ENSTA)    3 ECTS    code SU    MU5MEF26
• Geophysical and Astrophysical fluid dynamics (F. Petrélis & C. Gissinger – ENS)   3 ECTS  code SU    MU5MEF18
• Instabilities and control of shear flows (D. Sipp – ONERA)    3 ECTS    code SU    MU5MEF20
• Internal waves (S. Ortiz – ENSTA)    1,5 ECTS    code IPP    MEC664 IW
• Introduction to hydrodynamic instabilities (L. Lesshaft – X)    3 ECTS    code SU    MU5MEF19
• Micro-hydrodynamics (S. Michelin - X)    3 ECTS    code SU    MU5MEF40
• Multiscale Hydrodynamic Phenomena (P.Y Lagrée – SU)    3 ECTS    code SU    MU5MEF15
• Nonlinear waves and pattern formation  (S. Fauve – ENS)    3 ECTS    code SU    MU5MEF27
• Numerical Methods for fluid mechanics (S. Zaleski – SU)    3 ECTS    code SU    MU5MEF16
• Research in lab (teacher from one of the associated labs)     3 ECTS    code SU    MU5MEF24
• Turbulence Dynamics (B. Gallet – ONERA)     3 ECTS    code SU    MU5MEF22
• Vortices in Hydrodynamics (I. Delbende – SU)    3 ECTS    code SU    MU5MEF06

2nd semester (from March on)

• Internship, 30 ECTS (5-6 months)

Admission requirements

The program enlists students having a batchelor degree in mechanical engineering, physics or mathematics. Preferably, the batchelor's degree must correspond to four years of university education. A degree of exposure to basic fluid mechanics, numerical methods and to basic classical physics is required, as witnessed by grade transcripts.

Deadlines

If you reside abroad, first visit the page https://www.campusfrance.org/en . For some countries, there is a very early deadline before which you have to apply for the so-called CEF. The applications begin in December and the deadlines vary country by country, they can be as early as early March for some countries or even earlier, please check. 

To apply, you should also write an email to the program director, Stéphane Zaleski , preferably before the end of April. The applications committee will reply by early March or earlier by email. In some cases the committee will require the student to visit for an interview. If you are approved, the committee will send a support letter that you can use for your CEF interview if you are in a CEF country.

Application file

Formal applications open in May for the academic year 2021-22. It is not possible to apply directly if you are from a CEF country: in that case apply directly through CampusFrance. After the applications open, go to the dedicated web site. Select "M2 Mécanique : Mécanique des fluides Fondements Applications" and go through the steps. Do not forget to fill in the tab "Formulaires complémentaires" and specify "Fluid Mechanics". It you have trouble with this procedure or wish to know whether your applications has a reasonable chance of success write an email to Stéphane Zaleski . Fees for study at Sorbonne University are minimal.

Accommodation

 A lot of informations are available on the website of the "cité internationale universitaire de Paris". If you require help for housing ask well in advance, before May 30.