CEA/STMF develops computational fluid dynamics (CFD) codes in thermohydraulics that aim to quantify mass and energy transfers in nuclear cycle systems such as reactors and management devices of radioactive wastes. This thesis focuses on Lattice Boltzmann Methods (LBM) adapted to Adaptive Mesh Refinement (AMR) inside a generic computing environment based on Kokkos and executable on multi-GPU supercomputers. The proposed work consists in developing LB methods in the Kalypsso-lbm code to simulate coupled partial differential equations (PDEs) modelling incompressible two-phase and multi-component flows such as those encountered in downstream cycle devices. Once the developments have been completed, they will be validated with reference solutions. They will allow a comparison of various interpolation methods between blocks of different sizes in the AMR mesh. A discussion will be held on the refinement and de-refinement criteria that will be generalized for these new PDEs. Finally, benchamrks of performance will quantify the contribution of AMR for 3D simulations when the reference simulation is performed on a static and uniform mesh. This work will use supercomputers which are already operational (e.g., Topaze-A100 from CEA-CCRT), as well as the future exascale supercomputer Alice Recoque depending on the progress of its installation.