A fast algorithm for mass transfer on an unstructured grid formed by DEM particles
The Discrete Element Method (DEM) was used to generate a particle packing and transient mass transfer in the particle layer was simulated using a novel algorithm for determining the mass fluxes between DEM particles. This method is intended for simulating diffusion phenomena occurring during the dissolution of swelling polymers as the DEM particles can change size and distort the grid, whilst maintaining sharp boundaries between mesh elements. In this work, the robustness and accuracy of the algorithm was tested by solving a diffusion problem over the DEM mesh and comparing it to an accurate solution obtained by a finite difference (FD) approximation, whose discretisation was 10 times finer than that of the unstructured grid.
Parametric studies were conducted where the random packing and the size distribution of the DEM particles were altered and the differences in concentration profiles were compared with the FD reference solution through the use of the mean squared error. Both steady state and transient cases were compared. Two methods to improve the accuracy of the DEM unstructured grid were devised and tested using porosity and tortuosity data. In one case the porosity and tortuosity were obtained from the steady-state simulations and in the other case, local convex hulls were used to calculate porosity. Although both these methods decreased the mean squared error up to a factor of two, they also resulted into increased complexity of the simulation. It was concluded that the use of an effective packing algorithm and a narrow particle size distribution are key to maintaining the accuracy of the DEM-generated unstructured grid method.
Keywords: Mass transfer, Discrete Element Method, Diffusion, Mathematical modelling, Algorithm