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We consider coupled models for particulate flows, where the disperse phase ismade of particles with distinct sizes. We are thus led to a system coupling theincompressible Navier-Stokes equations to the multi-componentVlasov-Fokker-Planck equations. We design an asymptotic-preserving numericalscheme to approximate the system. The scheme is based on suitable implicittreatment of the stiff drag force term as well as the Fokker-Planck operator,and can be formally shown to capture the hydrodynamic limit with time step andmesh size independent of the Stokes number. Numerical examples illustrate theaccuracy and asymptotic behavior of the scheme, with several interestingapplications.

Asymptotic-preserving schemes for kinetic-fluid modeling of mixture flows with distinct particle sizes