Asymptotic-Preserving Schemes for Kinetic-Fluid Modeling of Mixture Flows (Communications in Computational Physics, 2024)
We consider coupled models for particulate flows, where the disperse phaseis made of particles with distinct sizes. We are thus led to a system coupling the incompressible Navier-Stokes equations to the multi-component Vlasov-Fokker-Planckequations. We design an asymptotic-preserving numerical scheme to approximate thesystem. The scheme is based on suitable implicit treatment of the stiff drag force termas well as the Fokker-Planck operator, and can be formally shown to capture the hydrodynamic limit with time step and mesh size independent of the Stokes number.Numerical examples illustrate the accuracy and asymptotic behavior of the scheme,with several interesting applications.