The first aim of the exercices sessions is to learn the implementation of the finite element method for solving simplified one-dimensional problems arising from the Navier-Stokes equations. Starting from a steady diffusion problem, the aquarius code written in Matlab is gradually improved in order to solve the unsteady Burgers equation.

As a second step, multi-dimensional problems of increasing complexity are solved using the open source finite element code freefem++ with the aim of solving the unsteady Navier-Stokes equations.

Finally, a project using the comercial finite-element code COMSOL is proposed. The aim is to solve multiphysical problems such as non-isothermal fluid flows or fluid-solid interaction.

The advantage of high-order methods, the influence of various numerical parameters and stabilisation techniques are also discussed with a practical approach using these three codes.

aquarius exercises
01.10.2009  Steady diffusion problem
08.10.2009  Steady advection diffusion problem and upwinding
15.10.2009  Unsteady advection diffusion problem
22.10.2009  Burgers equation (Mini-project)

freefem++ exercises (gallery)
29.10.2009  Steady and unsteady diffusion problem
12.11.2009  Steady advection diffusion problem and stabilisation methods (presentation)
26.11.2009  Steady and unsteady Stokes and Navier-Stokes equations

COMSOL mini-projects '08