Mathematical modeling and numerics of particle-laden flows: unresolved CFD-DEM

The problem of simultaneous flow of a fluid and a granular material is one of large interest
to natural scientists and engineers alike. In this thesis we deal with the mathematical
modeling and numerics for this problem. Recent advances in computing allow tracking
large numbers of particles in a Lagrangian manner by the so-called discrete element method
(DEM), while solving for the fluid flow field by standard methods of computational
fluid dynamics (CFD). After briefly discussing various approaches to this problem, we
look in detail at the so-called unresolved CFD-DEM paradigm, which employs a volumeaveraged
version of the Navier-Stokes equations (VANS). We derive the VANS equations
by using the theory of distributions as introduced by Schwartz and then examine how
the VANS equations are coupled to particle calculations when obtaining a numerical
solution. Finally, we compare some methods for calculating the volume fraction.