This research proposal focuses on the study and implementation of polytopal methods for solving the equations of fluid mechanics. These methods aim to handle the most general meshes possible, overcoming geometric constraints or those inherited from CAD operations such as extrusions or assemblies that introduce non-conformities. This work also falls within the scope of high-performance computing, addressing the increase in computational resources and, in particular, the development of massively parallel computing on GPUs.

The objective of this thesis is to build upon existing polytopal methods already implemented in the TRUST software, specifically the Compatible Discrete Operator (CDO) and Discontinuous Galerkin (DG) methods. The study will be extended to include convection operators and will investigate other methods from the literature, such as Hybrid High Order (HHO), Hybridizable Discontinuous Galerkin (HDG), and Virtual Element Method (VEM).

The main goals are to evaluate:
1. The numerical behavior of these different methods on the Stokes/Navier-Stokes equations;
2. The adaptability of these methods to heterogeneous architectures such as GPUs.