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

TL;DR

This paper develops an asymptotic-preserving numerical scheme for coupled kinetic-fluid models of particulate flows with different particle sizes, effectively capturing the hydrodynamic limit regardless of the Stokes number.

Contribution

It introduces a novel implicit scheme that handles stiff terms and accurately models multi-size particle flows in a unified framework.

Findings

The scheme is stable and accurate across various regimes.

It successfully captures the hydrodynamic limit in simulations.

Numerical examples demonstrate the scheme's effectiveness.

Abstract

We consider coupled models for particulate flows, where the disperse phase is 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-Planck equations. We design an asymptotic-preserving numerical scheme to approximate the system. The scheme is based on suitable implicit treatment 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 and mesh size independent of the Stokes number. Numerical examples illustrate the accuracy and asymptotic behavior of the scheme, with several interesting applications.