Energy generation through combustion of hydrocarbons continues to dominate, as the most common method for energy generation. In the U.S. nearly 84% of the energy consump- tion comes from the combustion of fossil fuels. Because of this demand there is a continued need for improvement, enhancement and understanding of the combustion process. As computational power increases, and our methods for modelling these complex combustion systems improve, combustion modelling has become an important tool in gaining deeper insight and understanding for these complex systems. The constant state of change in computational ability lead to a continual need for new combustion models that can take full advantage of the latest computational resources. To this end, the research presented here encompasses the development of new models, which can be tailored to the available resources, allowing one to increase or decrease the amount of modelling error based on the available computational resources, and desired accuracy. Principal component analysis (PCA) is used to identify the low-dimensional manifolds which exist in turbulent combustion systems. These manifolds are unique in there ability to represent a larger dimensional space with fewer components resulting in a minimal addition of error. PCA is well suited for the problem at hand because of its ability to allow the user to define the amount of error in approximation, depending on the resources at hand. The research presented here looks into various methods which exploit the benefits of PCA in modelling combustion systems, demonstrating several models, and providing new and interesting perspectives for the PCA based approaches to modelling turbulent combustion. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

Dans le cadre de cette thèse, je m'intéresse à la gestion des combustibles fossiles (pétrole, gaz naturel, charbon) en présence d'interactions stratégiques entre diffé­rents types d'agents. Dans un premier temps, j'étudie sous quelles conditions deux firmes asymétriques, exploitant une ressource non renouvelable, peuvent s'entendre autour d'un accord de coopération et ainsi former un cartel. J'analyse en parti­culier l'ensemble des accords possibles ainsi que la possibilité que ceux-ci soient acceptés par toutes les parties prenantes. Dans un second temps, je m'intéresse plus spécifiquement à l'incitation des pays membres du cartel de l'Opep à sures­timer ou sous-estimer leurs réserves de pétrole depuis l'instauration du système des quotas de production en 1982. Enfin, je caractérise la politique optimale d'un gouvernement en faveur du développement des technologies backstop au travers de subventions en R&D afin d'assurer la transition énergétique depuis des énergies fossiles polluantes à des énergies renouvelables non polluantes. Mais, je fais cette analyse dans le contexte où la production est contrôlée par une firme indépendante et lorsque le gouvernement ne peut pas implémenter une taxe sur les émissions. Un point commun de ces trois chapitres est la présence d'agents ayant des intérêts divergents. D'un point de vue méthodologique, j'utilise la théorie des jeux et, en particulier, les jeux différentiels dans les deux premiers chapitres. / This dissertation provides an analysis of the management of fossil fuels (oil, gas, coal) in the presence of strategic interactions between different types of agents. First, I study under which conditions two asymmetric firms, extracting a nonre­newable resource, may agree upon a cooperative agreement and, thus, merge into a cartel. I analyse, in particular, the set of feasible agreements and the possibility that every players accept one of them. Second, I focus more specifically on the incentives for the Opec members to over-report or under-report their oil reserves since the set of production quotas in 1982. Third, I characterize the optimal policy of a government in favor of the developing of backstop technologies through R&D subsidies in order to ensure the ecological transition from polluting fossil fuels to non-polluting renewable energies. However, I conduct this analysis in the context where the supply is controlled by an independent firm and when the government cannot implement a Pigovian tax on emissions. A common theme of these dif­ferent chapters is the presence of agents whose interests are contradictory. From a methodological point of view, I use game theory and, in particular, differential games in the two first chapters.