Laboratoire IMATH

Résumé : I will present the work of my PhD thesis which was to develop a comprehensive theoretical and numerical framework for the semi-geostrophic equations of atmospheric dynamics, grounded in the theory of semi-discrete optimal transport. I will present a novel, mesh-free, 3D numerical scheme for the incompressible semi-geostrophic equations. This method is structurally energy-conserving, enabling robust, long-term simulations, as demonstrated by the first fully 3D simulation of a twin cyclone using a semi-discrete optimal transport approach. Second, I will discuss the global-in-time existence of weak solutions for the compressible semi-geostrophic equations with compactly supported, measure-valued initial data, and the complications that arise from introducing compressibility. Finally, I will present some early simulations of a 2D compressible slice model and its particle-based discretization, establishing the foundation for future 2D and 3D compressible simulations. Together, these contributions provide a unified and powerful approach for the analysis and simulation of large-scale atmospheric flows.