### Duration

26h Th, 26h Pr, 30h Proj.

### Number of credits

### Lecturer

### Language(s) of instruction

French language

### Organisation and examination

Teaching in the second semester

### Schedule

### Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

### Learning unit contents

The course provides a rigorous and systematic presentation of the basic concepts and classical mathematical models used in various fields of application of Newtonian fluid mechanics. These models, and their simplified versions, are used to better understand the underlying physical processes.

The following topics are addressed :

- Kinematics of fluid flows.
- Budget equations (local and integral forms) and associated boundary conditions. Newtonian fluid and Navier-Stokes equations.
- Vorticity dynamics and potential flow.
- Introduction to CFD.
- Flow regimes.
- Introduction to gas dynamics : total / sonic properties, normal and oblique shock waves, de Laval nozzle;
- Turbulence : characterization, log-law, closure models, RANS/LES/DNS simulations.
- Gravity waves, capillarity waves, internal waves;
- Introduction to geophysical fluid dynamics.

### Learning outcomes of the learning unit

At the end of the course, the student will master the basic concept of Newtonian fluid dynamics. He/She will be able to use both the tensor and indicial formalism to design mathematical models of most large scale and small scale flows. In particular, he/she will be able to make the link between the physical processes and their mathematical parameterization and to justify the main assumptions.

He/She will be able to write down budget equations, understand the processes responsible for the transport of information and energy in fluids, use integral forms of the Navier-Stokes equation to describe simple flows. He/She will also be able to rely on a simplified 1D model to describe shock waves in a nozzle.

Through the group project, the course contribute to the development of soft skills like self-study, collaborative work and reporting.

### Prerequisite knowledge and skills

A working knowledge of vector calculus (as taught for instance in MATH0002) and the basic concepts of continuous mechanics and tensor algebra (see MECA0001 and MECA0011) is required.

The course forms a preparation of the students to the systematic use of the concepts of fluid mechanics in the more specific contexts addressed in courses of aerodynamics, space propulsion, aircraft design, microfluidics, hemodynamics, blood geophysical fluid dynamics,...

### Planned learning activities and teaching methods

The course includes ex-cathedra lectures, exercise sessions and a simulation project. The three parts provide a coherent approach of the physics and of the mathematical and numerical modelling of flows.

- The physical processes and concepts, together with their mathematical modelling, are presented at the ex-cathedra lectures.
- During the exercise sessions, simple and classical problems are solved.
- The project, to be carried by groups of three students, opens the way to more complex flows using the open source software OPENFOAM. This provides a first contact with numerical fluid dynamics.

### Mode of delivery (face-to-face ; distance-learning)

Face-to-face learning.

### Recommended or required readings

Copy of the slides available at http://www.mmm.ulg.ac.be.

Reference for the lectures : Fluid mechanics (4th edition) de P.K. Kundu et I.M. Cohen (Academic Press, 2004, ISBN-13: 9780123737359) and F*luid mechanics (7th edition)* " de F. White (McGraw-Hill , 2011, ISBN-13: 978-0-07-352934-9)

Numerous applications are available in *Fluid Mechanics* de D. Pnueli et C. Gutfinger (Cambridge University Press, 1992, ISBN : 0-521-58797-2).

### Assessment methods and criteria

Written exams in June and in August/September (retake).

Both tests cover the theoretical aspects and the exercises. The official formulaire (Navier-Stokes equations in various coordinate systems, NASCA tables for compressible flows) can be used.

The simulation project accounts for 25 % of the global mark in June and September. If needed, the report can be modified in between.

The simulation project is a compulsory activity. Failure to produce a report will lead to a "A" as global mark.

### Work placement(s)

### Organizational remarks

The cours takes place during the second quadrimester only at a rate of one half a day per week (Thursday pm).

The schedule and organization details are available at http://www.mmm.ulg.ac.be/.

### Contacts

Prof. Éric J.M. DELHEZ
Institut de Mathématique, B37
Tél. 04/366.94.19
E.Delhez@uliege.be

List of assistants and contact details are available at http://www.mmm.ulg.ac.be/