Theoretical and Numerical aspects for incompressible fluids

M2, master Mathematiques et Applications, ANEDP
Sorbonne Université

Course instructors:
Class: wednesday 10:00-12:00, room 15-25 104

1. Syllabus

This class is an introduction to mathematical and computational aspects of incompressible fluid flow simulations. It is presented to the point of view that the students are (going to be) applied mathematicians, physicists or engineers.

Computational fluid dynamics is at the crossroad of many disciplines and, like many topics at the interfaces between disciplines, its access may seem a bit harsh for (under)graduate students in mathematics or engineering. Our goal is to cover the main aspects of finite element methods for incompressible flows. We have sought to achieve a right balance between theoretical concepts, numerical analysis, description of schemes and algorithms and engineering applications. Numerical experiments using FreeFem++ will help students to understand these concepts and see advanced numerical methods in action.

  1. A fluid mechanics primer
  2. The Stokes model
  3. The Navier-Stokes model
  4. Two-fluid or two-phase flows
  5. Shape optimization for fluids
  6. Appendix

2. Material

Students can download

3. References

4. Research papers

Méthode de porosité Optim. de forme appliquée au design de bypass ou à la forme de l'arbre bronchique Algorithmes numériques en optim. de forme Contrôle optimal sous contrainte NS et influence des Riblets sur un conduit Modélisation du poumon/arbre bronchique Méthodes de type level set et applications Optimalité des maillages Méthodes des caractéristiques pour NS Méthodes de projection pour NS Optimisation de formes, applications biomédicales Optimisation de formes appliquée

All papers can be accessed in PDF format following this link-> list

5. Grading

Written exam + oral presentation.

Updated 2022-01-21 09:04 CET