Course Director(s): Olivier Bonnefoy et Sylvain MARTIN

Fluid mechanics are dealt with in this Toolbox from a mechanical statistics angle (Boltzmann equation) with a “Physics” type approach rather than that of an “Engineer”.
On completion of the Toolbox the student will be capable of:

1. Understanding the strong link between fluid mechanics and mechanical statistics
2. Enriching the physical terms of Navier-Stokes equations
3. Predicting the behaviour of a dynamic system, its stability and the transition mechanism towards chaos
4. Applying these concepts to describe complex systems (small Knudsen number flows, compressible fluids, granular flows)

The theoretical tools presented in the course will be applied in supervised study sessions in the computer room. The student will write a software programme with Matlab based on the LBMethod for modelling fluid flows in a pipe, around an obstacle or in a porous medium.

The Toolbox is structured around three unit sessions of equal importance.
Unit : Instabilities and transitions (15 hours)

• Instability examples (Rayleigh-Bénard, laminar/turbulent, and/or others)
• “Non-standard” flows: small Knudsen number flows, compressible fluids)

Unit 2: From the Boltzmann equation to the Navier-Stokes equation

• Boltzman equation
• Passage from Boltzmann to Navier-Stokes
• Chapman-Enskog expansion for medium density media

Unit 3: Lattice Boltzmann method (LBM)

• Theory and algorithms
• Supervised studies with Matlab
• Application to von Karman vortices alley

Teaching extensions of the core curriculum course in Physics

Strong link with the “Multi-phase flow” unit of the Process engineering major

Mechanical statistics, fluid mechanics, dynamic systems, stability and transition towards chaos, Lattice Boltzmann Method, creation of a CFD software programme.