Écoles d'été - Ecoulements gravitaires et risques naturels

Programme provisoire

Contributions



Florian Blachère, LMJL, Université de Nantes, Admissibility and asymptotic-preserving scheme

Laurent Chiron, Hydrocéan, Ecole Centrale Nantes, Particle refinement in the SPH method: stability and CPU analysis

Laurent Chupin, Université Blaise Pascal, Clermont-Ferrand, A bi-projection method for Bingham type flows

Vivien Desveaux, INRIA, UMPC, Un schéma well-balanced pour le modèle de Ripa

Arnaud Duran, IMT, Université Paul Sabatier, Toulouse 3, Simulation numérique de modèles d'écoulements type depth averaged : une classe de schémas Volumes Finis et Galerkin Discontinu

Christophe Josserand, Institut d'Alembert, UPMC, Paris 6, Impacts de gouttes: étalement, splashes etc

Dena Kazerani, LJLL, UPMC, Paris 6, Structure symétrique des équations de Green-Naghi et application à la
stabilité asymptotique des équilibres du système avec viscosité

Nathan Martin, Institut de Physique du globe, Paris, Modelling of a viscoplastic granular column collapse and
investigation of the role of μ(I) rheology

Sébastien Martin, Université Paris Descartes, Direct simulation of rigide particles in a viscoelastic fluid

Jordan Mathé, Université Blaise Pascal, Clermont-Ferrand, Ecoulements de fluides de Bingham incompressibles non-homogènes à seuil variable et application à la volcanologie

Victor Michel-Dansac, LMJL, Université de Nantes, A well-balanced scheme for the shallow-water equations with topography and bottom friction

Bijan Mohammadi, IMAG, Université de Montpellier, Dynamique bathymétrique par minimisation d'énergie et transport minimal

Pascal Richter, RWTH, Aachen, Numerical modelling of compressible two-phase
with two velocities, two pressures and source terms

Philippe Ung, MAPMO, Université d'Orléans, How to treat the coupling issue of the Saint-Venant-Exner
system of equations

Programme

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.

Programme des mini-cours

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