Le nouveau programme (mis à jour le 12/05 à 16h15) est à télécharger ici.

Les supports des présentations devront être en anglais. Les exposés pourront être donnés en français.

Analyse des effets des bords rugueux en mécanique des fluides

David Gérard-Varet, IMJ, Université Denis Diderot Paris 7

Mardi 02/06 de 14h30 à 16h, présentation 1/2
Mercredi 03/06 de 14h30 à 16h, présentation 2/2

Résumé : Nous discuterons dans ce cours l'effet d'une paroi rugueuse sur un fluide visqueux, /via/ une approche mathématique de type homogénéisation. Nous aborderons principalement deux problèmes :

1. La dérivation de lois de paroi. Il s'agit de remplacer dans les codes numériques la paroi rugueuse par une paroi lisse, en y imposant une condition aux limites effective, reflétant l'effet moyen de la rugosité.
2. Le lien entre rugosité et dissipation d'énergie. Nous évoquerons notamment le cas de fluides géophysiques (en rotation rapide), pour lesquels l'irrégularité du bord peut avoir l'effet paradoxal de réduire la friction.

Gravity driven flows on planets: process diversity and formation conditions

Nicolas Manglod, LPG, CNRS & Université de Nantes

Lundi 01/06 de 14h à 16h, cours

Résumé : Mass wasting processes are a strong agent of erosion on Earth, as is the case on other planets. In this lecture we will discuss the formation of mass flows in various planetary surfaces such as Mars, the moon and asteroids. For instance, Mars displays a strong variety of mass flows from <1 km small volatile-rich gullies to giant > 100 km long dry landslides. The differences in temperature and pressure conditions, gravity, and volatile types, create a zoo of landforms that enlarges the range of physical parameters in which mass flows can be observed on Earth, questioning some fundamental aspects of their formation.

Numerical algorithms in viscoplastic fluids: from 3D to thin layers

Pierre Saramito, LJK, CNRS & Université de Grenoble

Mardi 02/06 de 9h à 10h30 Mercredi 03/06 de 9h à 10h30, notes de cours

Short introduction (five slides) available here.

The aim of this lecture is to study viscoplastic fluid models and their numerical resolution. Viscoplastic flow problems are motivated by environmental applications: snow avalanches, mud or ice flows, volcanic lavas, granular flows. Most of some fluids of the common life, such as toothpaste, hair gel, clay, cement and blood are viscoplastic fluids. These materials behave as a rigid solids when the applied stress is below a yield value and as a fluids otherwise. From mathematical point of view, viscoplastic problems are defined by a minimization of a non-differentiable functional, related to the dissipation of energy. For simple shear flows, such as the Poiseuille or Couette flows, explicit computations are presented. For more complex and general flows conditions, the explicit computation of the solution is no more possible and we are looking to build some approximation. For viscoplastic fluids, the numerical approximation requires some specific tools. Two main classes of numerical algorithms are presented: the regularization method and the augmented Lagrangian algorithm. This second approach uses some convex analysis tools that are also introduced in this lecture. Equations and models are presented in a continuum setting, and then approximated in time and space. Numerical approximations are demonstrated together with software solutions based on auto-adaptive mesh methods for several examples of practical interest. The study of shallow approximations of viscoplastic fluids is motivated by many geophysical applications such as landslides, mud flows, snow avalanches and volcanic lava flows. The lecture develops an asymptotic analysis for these thin viscoplastic flow problems: in that case, the three-dimensional problem could be reduced to a two-dimensional surface one. Numerical approximations of thin viscoplastic problems are demonstrated for volcanic lava flow and simulations are compared with physical observations.

Persons who complete the course will have demonstrated the ability to do the following:

• formulate and solve nonlinear physical and mechanical problems.
• demonstrate a familiarity with fluid mechanics and complex materials
• synthesize and implement efficient algorithme for various applications