Description of the thesis topic

The aim of this thesis is to take wall effects into account in natural flow models. The subject will focus on the basal part of dense granular flows generated during explosive volcanic eruptions. These flows are known to be destructive and to travel distances that can exceed 100 kilometres on almost horizontal slopes. Recent theoretical and experimental work has shown that it is essential to take better account of the boundary conditions, i.e. the interaction of the granular medium with all the walls, to describe the dynamics of these flows. A law has been proposed and its validity has been experimentally confirmed, but it has not yet been implemented in a continuous model: this is the subject of this thesis. A complete study from theoretical analysis to implementation in a numerical scheme for comparison with experimental measurements. The use of models, based on the incompressible Navier-Stokes equations with a specific rheology, is crucial in this context. One of the key points of the thesis will be to include the new wall law, to propose a theoretical analysis of the model (existence, uniqueness of solution), to discuss a suitable and efficient numerical scheme (stability study, convergence) and to help with the implementation to visualise the effects on simulated flows. Experimental data supplied by the Magmas and Volcanoes Laboratory (UCA) will be used to validate the numerical simulations.

Work Context

Laboratoire de Mathématiques Blaise Pascal, Université Clermont Auvergne, Campus des Cézeaux, AUBIERE
Research team : Equations aux Dérivées Partielles et Analyse Numérique (EDPAN)

The position is located in a sector under the protection of scientific and technical potential (PPST), and therefore requires, in accordance with the regulations, that your arrival is authorized by the competent authority of the MESR.