Thomas Bellotti rejoindra en octobre l'EM2C en tant que chargé de recherche CNRS.
Titre : Numerical analysis of general lattice Boltzmann schemes and boundary conditions for a two-unknowns method
Résumé : In this talk, I will first present key results from our recent works on the numerical analysis of lattice Boltzmann schemes, which ignore boundary conditions. These schemes can be used to simulate systems of conservation laws. Next, I will theoretically examine boundary conditions in lattice Boltzmann methods, focusing on a simplified two-unknowns model. By mapping lattice Boltzmann schemes to finite difference schemes, we enable rigorous consistency and stability analyses. We propose kinetic boundary conditions for inflow and outflow scenarios, addressing the trade-off between accuracy and stability, which we successfully mitigate. Consistency is analyzed using modified equations, while stability is assessed via GKS (Gustafsson, Kreiss, and Sundström) theory. For coarse meshes, where GKS theory may falter, we employ spectral and pseudo-spectral analyses of the scheme's matrix to explain low-resolution effects. Lastly, I will discuss potential research directions related to boundary conditions in kinetic schemes.