Modélisation multiphysique de l'écoulement des glaciers : analyse et résolution numérique d'un problème couplé non linéaire

Multiphysics modelling is concerned with systems that couple multiple physical phenomena
(mechanics, heat transfer, electromagnetism, hydrodynamics, . . . ) as well as with the interaction
between multiple individual components. Multiphysics modelling is interested in finding
efficient numerical methods to deal with the coupling between the different components of
a complex system. Interest in multiphysics simulations is steadily increasing as numerous
current scientific problems involve multiple physical components. Among current issues, icesheet
and glacier numerical models have become essential to predict the evolution of ice sheets
as a result of global warming. Ice flow is usually described as a gravity-driven creep flow of
a nonlinearly viscous fluid. Detailed glacier models need to account for temperature dependence
of ice viscosity, which leads to a thermomechanical coupled model for ice flows. This
final-year project addresses the analysis of a stationary thermomechanical glacier model as an
example of a multiphysics problem. The goal will be to provide a physical, mathematical and
numerical framework for future development in glaciology and in multiphysics simulations
more generally. Thus this thesis is divided into three main parts. The first part addresses the
physical description and modelling of glaciers. The second part is devoted to the theoretical
study of numerical methods for the mechanical and thermal problems. Classical finite element
methods will be presented as well as new research perspectives. The third part is concerned
with the application of these multiphysics methods to an alpine glacier model. This third part
highlights the importance of tightly coupled methods as new opportunities for multiphysics
simulations.