This thesis builds upon X-Mesh, a recent finite element method that allows the controlled use of degenerate elements to maintain a continuous, sharp representation of moving interfaces in two-phase flow simulations.
 We develop new mesh deformation algorithms tailored to this framework, enabling accurate interface tracking without resorting to global remeshing.

A second contribution is the development of a mathematical theory for zero-measure elements, leading to the Tempered Finite Element Method (TFEM), which ensures stable and convergent FEM computations even when degenerate elements arise.

Finally, we apply the X-Mesh framework and TFEM to 2D two-phase flow problems, demonstrating their robustness and accuracy for interface-dominated fluid dynamics.

Membres du jury :

• Prof. Remacle Jean-François  (UCLouvain)(Promoteur)
• Prof. Ponthot Jean-Philippe  (ULiège)(Co-promoteur)
• Prof. Fisette Paul (UCLouvain) (Président)
• Prof. Rattez Hadrien  (UCLouvain) (Secrétaire)
• Prof. Moës Nicolas (UCLouvain)
• Prof. Lambrechts Jonathan (UCLouvain) 
• Prof. Moureau Vincent (CORIA)

Soutenance publique également accessible par visio-conférence via le lien (TEAMS) : 

https://teams.microsoft.com/light-meetings/launch?context=%7B%22Tid%22%3A%227ab090d4-fa2e-4ecf-bc7c-4127b4d582ec%22%2C%22Oid%22%3A%2247ed4810-3905-4765-b65a-cf4730504174%22%7D&anon=true&lightExperience=true&correlationId=18ba513b-6603-4396-99b5-30452d2a0563&agent=web&version=25111315502&coords=eyJjb252ZXJzYXRpb25JZCI6IjE5Om1lZXRpbmdfWldVM05XUmtOR010Wm1Jek5TMDBOalJtTFRobFl6VXRZVEJqTkRNMVkyWTJNekk1QHRocmVhZC52MiIsInRlbmFudElkIjoiN2FiMDkwZDQtZmEyZS00ZWNmLWJjN2MtNDEyN2I0ZDU4MmVjIiwib3JnYW5pemVySWQiOiI0N2VkNDgxMC0zOTA1LTQ3NjUtYjY1YS1jZjQ3MzA1MDQxNzQiLCJtZXNzYWdlSWQiOiIwIn0%3D&deeplinkId=00e74520-777f-4a02-8314-40b3e408e560