Spatial Filtering for Scale Bridging and its Application to Transport in Dense Particle Beds

We present the method of spatial filtering as a universal approach to support closure development for models of dense fluid-particle systems. Starting from a set of governing equations, we provide an overview of closures that are required at different levels of a model hierarchy. A focus is on closures to be used in meso-scale models, highlighting recent developments that aim at the description of the variability of exchange coefficients, as well as wall effects. Furthermore, attempts to describe the anisotropy of meso-scale stresses, as well as the effect of cohesive particle-particle interactions in the context of macro-scale models are summarized. Computational aspects, together with selected verification cases are documented to stimulate a broader use of the filtering approach. Finally, we outline three future research directions that appear most fruitful. These final thoughts may help to establish more reliable and robust multiphase flow models for reactive systems.