Simulation of Fluid–Particles Flows: Heavy Particles, Flowing Regime and Asymptotic-Preserving Schemes

We are interested in an Eulerian–Lagrangian model describing particulate flows. The model under study consists of the Euler system and a Vlasov-Fokker-Planck equation coupled through momentum and energy exchanges. This problem contains asymptotic regimes that make the coupling terms stiff, and lead to a limiting model of purely hydrodynamic type. We design a numerical scheme which is able to capture this asymptotic behavior, without requiring prohibitive stability conditions. The construction of this Asymptotic Preserving scheme relies on an implicit discretization of the stiff terms which can be treated by efficient inversion methods. This method is a natural coupling of a kinetic solver for the particles with a kinetic scheme for the hydrodynamic Euler equations. Numerical experiments are conducted to study the performance of this scheme in various asymptotic regimes.