Description du sujet de thèse

One of the most pressing challenges for the future of our planet is the development of a truly sustainable society. Addressing this challenge requires a strong commitment to researching innovative systems for green energy production, as well as effective strategies to reduce CO₂ emissions.
Hydroelectric power is a well-established and widely used source of clean energy, while the underground storage of CO₂ in depleted reservoirs is gaining recognition as a promising approach to mitigating greenhouse gas emissions. In both domains, advanced numerical methods play a pivotal role in understanding the underlying physical processes. They provide powerful tools for investigating, designing, and controlling complex systems in realistic operating conditions.
The physical phenomena involved are typically governed by nonlinear systems of partial differential equations. Classical numerical approaches based on finite volume and finite difference methods are commonly used to solve these models. Among them, semi-implicit time integration schemes offer significant advantages due to their enhanced stability properties, which can improve the overall computational efficiency of simulations.
The primary objective of this PhD thesis is the design, mathematical analysis, and implementation of advanced numerical schemes with provable asymptotic accuracy and structure-preserving properties at the discrete level. These methods will be specifically tailored to applications involving rotating turbomachinery systems used in hydroelectric power plants and the injection of CO₂ into geological reservoirs.
The project will be carried out in collaboration with internationally recognized research groups, including teams at Politecnico di Milano (Italy) and EPFL (Switzerland). These collaborations will provide opportunities to work closely with experts in the numerical simulation of turbomachinery and subsurface CO₂ storage, respectively.

Contexte de travail

The LAMA laboratory is a mathematics research institute located in Le Bourget-du-Lac near Chambéry. It has around thirty permanent members (researchers and teacher-researchers) working in the fields of pure mathematics, applied mathematics, and mathematics for computer science. The host team will be the PDEs² (EDPs²) team. The PhD student will work with scientists from Politecnico di Milano (Italy) and EPFL (Switzerland).

Contraintes et risques

Travel may be possible for participation in national or international scientific conferences.