TB2 - ADVANCED FLUID MECHANICS

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 hydrodynamics instabilities
   

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 LBM Method for modelling fluid flows in a pipe and around an obstacle, with or without thermal coupling.

The Toolbox is structured around two unit sessions :

Unit 1: From statistical physics to a CFD solver based on LBM (20 hours)

-Boltzmann equation and passage from Boltzmann to Navier-Stokes

-Design, writing and validation of a LBM solver

• Discretization of Boltzmann equation, algorithm and boundary conditions
• Writing of the code (hands on computer with matlab)
• Validation on simple test cases

Unit 2: Hydrodynamic instabilities: theory and numerical analysis (20 hours)

-Dynamical systems and linear stability analysis

-Case study: with the LBM code, study of one instability such as Rayleigh-Plateau, Rayleigh-Bénard or von Karman vortex street

Teaching extensions of the core curriculum course in Physics