Contributions to hydrodynamic and geochemical modeling of fluids: from digital approaches to applications

The equations of Fluid Mechanics are strongly nonlinear equations for which, in general, analytical solutions are not available. They must therefore be solved numerically using suitable methods. This dissertation presents a selection of my research activities, which have involved equating problems involving fluid flow or the transport of chemical species, and then solving these systems of equations using numerical analysis techniques. The common thread of this work is therefore the use of modeling and numerical simulation to understand complex phenomena. The first part of this dissertation presents a notice of my titles and works. In the second part, devoted to the assessment of my research work, I chose to detail my contributions in the following three areas: - modeling of hydrodynamic instabilities; - modeling of surface and underground flows; - modeling of reactive transport in porous media. In the chapter devoted to the modeling of hydrodynamic instabilities, I present my research activities on the deterministic phase of development of the Richtmyer-Meshkov instability, a particular hydrodynamic instability which appears when an interface separating two fluids of different densities is subjected to an 'impulse' acceleration created, for example, by the passage of a shock wave. In the chapter devoted to my work in modeling surface and underground flows, I present a new expression for the friction coefficient as a function of the water height in the flowing water layer. This expression was established and validated through surface flow and transport experiments of a non-reactive tracer on an instrumented plot. I then recall some work that I have carried out in hydrogeology for the problem of geological storage of nuclear waste. In the chapter devoted to my contributions in modeling reactive transport in porous media, I first present the modeling of geochemistry-transport coupling and the digital tools that I have developed for the problem of nuclear waste storage. Then I show the interest of these tools for other applications in the field of geosciences. Finally, in the third and final part of this dissertation, I outline some perspectives linked to the three scientific aspects that I chose to present in the review of my previous work. These perspectives concern: - the study of convective instabilities, sources of oceanic hydrothermalism; - modeling of the geochemistry-transport coupling leading to the release of hydrogen at the Mid-Atlantic Ridge; - modeling the coupling between surface and underground flows