MEC432 - Mécanique des fluides (2023-2024)

Fluid mechanics is at the center of many engineering and research applications.

The course aims to establish and consolidate the fundamentals of this discipline. It is designed to appeal both to students who wish to limit themselves to obtaining a general and rigorous education on the subject, and to students who plan to pursue one or more in-depth studies in this specialty next year.

The MEC432 fluid mechanics course lays the basics of this discipline. The course begins by putting the notion of fluid into perspective with regard to physics and thermodynamics:

what distinguishes a fluid from a solid? What distinguishes different fluids? What is a Newtonian fluid?

We will then explain the fundamental principles of fluid flow kinematics, those of dynamics and energetics, to arrive at the fundamental equations of Newtonian fluid mechanics: the Navier-Stokes equations. These equations, although reputed to be among the most difficult in physics, are analyzed and calculated by engineers and researchers on a daily basis. We will present the approximations that ease this, notably the one of the "incompressible fluid" and of the "perfect fluid", insisting on their physical conditions of validity.

We'll then study how can the complexity of these problems be further reduced, sometimes to the point of no mathematical resolution at all, thanks to dimensional analysis and the principles of similarity on which fluid mechanics experimentation is based.

We'll then take a closer look at the perfect-fluid approximation that forms the major part of many historical applications of fluid mechanics. The analysis of perfect-fluid flows highlights the special role of vorticity, and we will explore "vorticity dynamics", which can be considered a discipline.

We will then show how the perfect-fluid approximation can be connected to another approximation that concentrates most of the effects of viscosity, the boundary-layer approximation, in order to obtain a uniformly valid description of any flow.

Finally, the course will end with an introduction to turbulence, one of the main frontiers in our understanding of fluid mechanics today.

Course language : French

ECTS credits : 5