Simulation of fluid and particles flows: Asymptotic preserving schemes for bubbling and flowing regimes

In this work, we propose asymptotic preserving numerical schemes for the bubbling and flowing regimes of particles immersed in a fluid treated by two-phase flow models. The description comprises compressible Euler equations for the dense phase (fluid) and a kinetic Fokker–Planck equation for the disperse phase (particles) coupled through friction terms. We show numerical simulations in the relevant case of gravity in the one-dimensional case demonstrating the overall behavior of the schemes.