Dans cette thèse on s’intéresse à la simulation numérique d’écoulements des matériaux compressibles, voir fluides et solides élastiques. Les matériaux considérés sont décrits avec un modèle monolithique eulérian, fermé avec une loi d’état hyperélastique qui considère les différents comportements des matériaux. On propose un nouveau schéma de relaxation qui résout les écoulements compressibles dans des différents régimes, avec des nombres de Mach très petits jusqu’à l’ordre 1. Le schéma a une formulation générale qui est la même pour tous le matériaux considérés, parce que il ne dépend pas directement de la loi d’état. Il se base sur une discrétisation complétement implicite, facile à implémenter grâce à la linéarité de l’opérateur de transport du système de relaxation. La discrétisation en espace est donnée par la combinaison de flux upwind et centrés, pour retrouver la correcte viscosité numérique dans les différents régimes. L’utilisation de mailles cartésiennes pour les cas 2D s’adapte bien à une parallélisation massive, qui permet de réduire drastiquement le temps de calcul. De plus, le schéma a été adapté pour la résolution sur des mailles quadtree, pour implémenter l’adaptativité de la maille avec des critères entropiques. La dernière partie de la thèse concerne la simulation numérique d’écoulements multi-matériaux. On a proposé une nouvelle méthode d’interface “sharp”, en dérivant les conditions d’équilibre en implicite. L’objectif est la résolution d’interfaces physiques dans des régimes faiblement compressibles et avec un nombre de Mach faible, donc les conditions multi-matériaux sont couplées au schéma implicite de relaxation. / In this thesis we are concerned with the numerical simulation of compressible materials flows, including gases, liquids and elastic solids. These materials are described by a monolithic Eulerian model of conservation laws, closed by an hyperelastic state law that includes the different behaviours of the considered materials. A novel implicit relaxation scheme to solve compressible flows at all speeds is proposed, with Mach numbers ranging from very small to the order of unity. The scheme is general and has the same formulation for all the considered materials, since a direct dependence on the state law is avoided via the relaxation. It is based on a fully implicit time discretization, easily implemented thanks to the linearity of the transport operator in the relaxation system. The spatial discretization is obtained by a combination of upwind and centered schemes in order to recover the correct numerical viscosity in different Mach regimes. The scheme is validated with one and two dimensional simulations of fluid flows and of deformations of compressible solids. We exploit the domain discretization through Cartesian grids, allowing for massively parallel computations (HPC) that drastically reduce the computational times on 2D test cases. Moreover, the scheme is adapted to the resolution on adaptive grids based on quadtrees, implementing adaptive mesh refinement techinques. The last part of the thesis is devoted to the numerical simulation of heterogeneous multi-material flows. A novel sharp interface method is proposed, with the derivation of implicit equilibrium conditions. The aim of the implicit framework is the solution of weakly compressible and low Mach flows, thus the proposed multi-material conditions are coupled with the implicit relaxation scheme that is solved in the bulk of the flow.

Public transport in many Sub-Saharan African cities consists of paratransit, mini-to-medium-sized buses, which provide public transport and operate demand-driven and unscheduled. This form of public transport is often seen as less safe, less dependable, and environmentally unfriendly. One common intervention is the development of a Bus Rapid Transit system. A Bus Rapid Transit system is characterized by its bus-only lanes and offers a cheaper solution to rail transit systems. The development of such a BRT system changes the structure of the public transport system as BRT often takes over the areas in which paratransit previously operated. This leads to clashes between the stakeholders of the two modes of transport, which can threaten the success of the system as well as the livelihood of the paratransit workforce. This paper uses socio-technical transition theory, as well as stakeholder theory, to provide a clear picture of the entire land passenger mobility system. The focus of this thesis lies on firstly, analyzing the question why the development of BRT is favored over the optimization of paratransit. Secondly, it looks at different interaction approaches between the multi- regimes scheduled public transport (BRT) and paratransit, which can lead to a successful public transport system. Lastly, socio-technical barriers (political, technical, socio-cultural, and economic) are analyzed to understand which obstacles have to be overcome and what corresponding measures are. The results show that the development of Bus Rapid Transit is favored over the optimization of paratransit. Paratransit is seen as unsafe and unreliable, while Bus Rapid Transit offers an efficient, reliable, eco-friendly solution which also targets vulnerable groups. Out of the four different interaction approaches, competition between BRT and paratransit, a hybrid form between paratransit and BRT, the replacement of paratransit, and the prohibition of paratransit, the hybrid form is seen as most successful, as it allows both systems to contribute their strengths. Lastly, the actors involved in the socio-technical system, and socio-technical barriers and corresponding measures were analyzed. The biggest take-away when looking at the actors of the land passenger mobility system is that all stakeholders have to be involved, which includes paratransit drivers and people working on and off the vehicles. This paper has shown that when these stakeholders are not included, there might be resistance that might compromise the success of the BRT. The socio-technical barriers used were divided into economic, financial, infrastructural, and socio-cultural barriers. A successful paratransit / BRT interaction benefits from the move from a target system to a monthly salary for the paratransit driver. There should both be regulations and incentives so that paratransit acts as a reliable partner for the BRT system. It should be noted that a successful BRT / paratransit interaction cannot easily be replicated in another country without looking at the urban form preconditions. Bus Rapid Transit is a feasible solution for many Sub-Saharan cities. For an encompassing public transport system to be successful and to outcompete the car, it is necessary that all stakeholders work together and contribute with their strengths.