Towards multiscale lattice Boltzmann modeling of granular flows

Granular flows are widely encountered in nature and in industries such as geotechnical engineering, pharmaceutical industry and food production. It is therefore of key importance to understand the complex granular flow behaviors at the grain scale and to carry out numerical simulations, especially at a full-scale, for effcient hazard mitigation and manufacturing process. Granular materials can behave as solids, liquids and gases depending on the flow regime, which complicates the relevant constitutive relations. In this talk, dfferent numerical techniques will be introduced to simulate the unsteady granular column collapse. In the dry scenario, where the interstitial air plays a negligible role, one-to-one discrete element simulations can be carried out such that the collapse dynamics and the final deposit are well reproduced compared to the experimental observations. In immersed granular collapses, the interstitial fluid has significant inertial and viscous effects on the motion of particles. The complex fluid-particle interactions, for instance the erosion of granular free-surface, can be well captured by coupling the computational fluid dynamics approach and the discrete element method (CFD-DEM). When CFD is coupled with DEM, a semiempirical drag model is required to calculate the hydrodynamic forces between the fluid and the particles. Alternatively, we can also couple the lattice Boltzmann method (LBM) with DEM, in which the complex fluid-particle interactions (both drag force and torque) are fully resolved based on the fundamental law of momentum conservation. The LBM-DEM formulation can be used to investigate the effects of initial packing density and column size, which heavily depend on the local interactions between the pore fluid and the solid particles, and between the flowing mass and the fixed rough bed. However, large-scale numerical simulations of granular flows, such as rock avalanches and industrial handling of granular materials, using the discrete approaches are still prohibitive due to the high computational cost, which necessitates efficient and accurate continuum simulations. The abovementioned LBM has so far been proven to yield accurate results comparable to the conventional computational fluid dynamics based on the Navier-Stokes equations and could be several orders of magnitude faster in terms of the computational speed. The conceptually simplest granular flow constitutive model, i.e., the so-called $\mu(I)$ rheology, has been implemented into LBM as our first step towards multiscale lattice Boltzmann modeling of granular flows.