Title: Impact crater relaxation throughout the Solar System Author: Martin Kihoulou Department: Department of Geophysics Supervisor: RNDr. Klára Kalousová, Ph.D., Department of Geophysics Abstract: In this thesis, we study the viscous relaxation of an impact-deformed icy shell of a dwarf planet Pluto. Motivation for this work is the position of Sputnik Planitia, a 1000 km wide, nitrogen-filled elliptic basin, which is located very close to Pluto-Charon tidal axis. Given this unlikely position on Pluto's sur- face, it was suggested that the basin was formed elsewhere and the whole body reoriented afterwards. For the reorientation to occur, the basin has to generate a positive gravity anomaly for which a combination of impact-related subsurface ocean uplift, ejecta blanket and accumulation of nitrogen ice was suggested. How- ever, to maintain the orientation towards the minimum principal axis of inertia until today, the ocean uplift must be present on timescales of billions of years, which may be achieved due to an insulating layer of high viscosity clathrates at the ice/ocean interface. We solve Pluto's ice shell evolution by the finite element method in 2D spherical axisymmetric geometry with an evolving free surface and assuming a viscous rheology. Our results show that the thermal effect of the im- pact...

Ce sujet de thèse s’inscrit dans le cadre des études actuellement menées au CEA/DAM concernant des schémas numériques ALE (Arbitrary-Lagrangian-Eulerian)de type « Lagrange + Projection », dans le contexte des simulations hydrodynamiques mutli-matériaux en grandes déformations. Ces schémas doivent respecter les équations de conservation de la masse, de la quantité de mouvement et de l’énergie totale.Les schémas décalés en temps et en espace sont très utilisés dans les codes industriels. Ils sont robustes et permettent une bonne approximation des comportements complexes, mais sont connus pour ne pas conserver exactement l’énergie totale. Cela pose un problème dans le traitement des chocs, sur maillages raffinés ou dans la simulation des milieux réactifs.En 2016, des travaux originaux on été proposés par A. Llor et. al. pour rendre conservatif ce type de schéma dans un contexte lagrangien (sans projection), notamment en proposant une correction pour retrouver la conservation de l’énergie totale.Le travail de cette thèse a été d’étendre ce schéma lagrangien dans un contexte ALE multi-matériaux (avec interface), en garantissant la conservation de toutes les quantités, le respect du second principe de la thermodynamique et la robustesse. De nombreux cas tests ont été menés (en 2D plan et en 2D axisymétrique) et comparés aux méthodes existantes afin de montrer la pertinence de cette approche. / This PhD subject comes within actual studies managed by CEA/DAM about ALE (Arbitrary-Lagrangian-Eulerian) schemes (with a splitting of Lagrangian and Remapping steps) in the context of hydrodynamic simulations. These numerical schemes have to respect mass, momentum and total energy conservation, which are the fundamental equations of the studied systems.Space- and Time-Staggered are widely used in industrial codes for their simplicity androbustness despite their known lack of exact energy conservation. This is a major drawbackin presence of strong shocks. Among all existing schemes, none of them meet the expectations of robustness, conservation,thermodynamic consistency (both shocks and relaxations capture), accuracy andadaptibility to complex behaviors. Recently, some novel works have been proposed by A.Llor et. al. in order to make conservative this type of scheme in a Lagrangian context (without remapping step). Current remap methods, necessary in large deformations, donot guarantee simultaneously total energy conservation and thermodynamic consistency.This work aims at extending this conservative Lagrangian space- and time-staggeredscheme to a multi-material ALE methodology, keeping its good properties (conservation,accuracy, thermodynamic consistency, robustness) intact. Classical, but demanding, test cases have been performed (both in plane and axisymmetric 2D geometries) and have been compared to existing numerical methods in order to assess the relevance of our approach.