In this work, a coarse-graining method previously proposed by the authors in
a companion paper based on solving diffusion equations is applied to CFD-DEM
simulations, where coarse graining is used to obtain solid volume fraction,
particle phase velocity, and fluid-particle interaction forces. By examining
the conservation requirements, the variables to solve diffusion equations for
in CFD-DEM simulations are identified. The algorithm is then implemented into a
CFD-DEM solver based on OpenFOAM and LAMMPS, the former being a
general-purpose, three-dimensional CFD solver based on unstructured meshes.
Numerical simulations are performed for a fluidized bed by using the CFD-DEM
solver with the diffusion-based coarse-graining algorithm. Converged results
are obtained on successively refined meshes, even for meshes with cell sizes
comparable to or smaller than the particle diameter. This is a critical
advantage of the proposed method over many existing coarse-graining methods,
and would be particularly valuable when small cells are required in part of the
CFD mesh to resolve certain flow features such as boundary layers in wall
bounded flows and shear layers in jets and wakes. Moreover, we demonstrate that
the overhead computational costs incurred by the proposed coarse-graining
procedure are a small portion of the total costs in typical CFD-DEM simulations
as long as the number of particles per cell is reasonably large, although
admittedly the computational overhead of the coarse graining often exceeds that
of the CFD solver. Other advantages of the present algorithm include more
robust and physically realistic results, flexibility and easy implementation in
almost any CFD solvers, and clear physical interpretation of the computational
parameter needed in the algorithm. In summary, the diffusion-based method is a
theoretically elegant and practically viable option for CFD-DEM simulations