Séminaire EDP, Modélisation et Calcul Scientifique (commun ICJ & UMPA)

Constrained minimization and Lagrange multipliers for the solution of flow problems with rigid particles: from granular dynamics to inertial suspension flows

par Anthony Wachs (UBC, Vancouver)

4e étage, salle 435 (UMPA, ENS Lyon - Site Monod)

4e étage, salle 435

UMPA, ENS Lyon - Site Monod

ENS de Lyon, 46 Allée d'Italie
Particle-laden flows are ubiquitous in environmental, geophysical and engineering processes. The intricate dynamics of these two-phase flows is governed by momentum transfer between the continuous fluid phase and the dispersed particulate phase. When significant temperature differences exist between the fluid and particles and/or chemical reactions take place at the fluid/particle interfaces, the two phases also exchange heat and/or mass, respectively. When the fluid exhibits non-Newtonian properties and in particular yield stress properties, particles can be trapped in the fluid. In this talk, I present various numerical models and computational strategies that we have been developing over the years to solve particle-laden flow problems. Many of these problems can be formulated as a constrained minimization and solved as a saddle-point problem with a robust Uzawa-like algorithm. Robust convergence is a particularly suitable property for massively parallel computing, sometimes at the expense of a lower computing speed. All over the talk, I illustrate on assorted examples of flow configuration the physical insight we are able to gain with our computational tools. Finally, I address the question of embedding the various numerical models into a comprehensive bottom-up multi-scale approach and discuss what we can expect from such an endeavour.
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