A meshless Lagrangian particle-based porosity formulation for under-resolved generalised finite difference-DEM coupling in fluidised beds

An under-resolved coupling strategy for the discrete element method (DEM) and the weakly compressible (WC) generalised finite difference method (GFD) is proposed. A novel filtering technique is proposed that allows for the recovery of a continuum porosity field in an arbitrary domain from DEM information. This allows fine spherical DEM particles to be treated in an under-resolved fashion using well-established drag relations for dynamic porous media to determine the fluid forces acting on them. To handle the momentum balance between phases, an inter-phase momentum transfer scheme is proposed as well. Verification and validation of the coupling strategy is performed. This includes comparisons to a fully-resolved WCGFD scheme when the associated computational cost allows for it. This strategy's benefits are seen when simulating a fluidised bed with an evolving fluid domain. It is shown that both under-resolved and fully-resolved dynamic information can seamlessly be treated with this scheme.