Discrete particle methods that track the motion of individual particles and their collisions are computationally very expensive. To accelerate these numerical simulations, some basic assumptions have been introduced and reported in the literature. This study investigates two of these common assumptions: (1) the use of computational parcels, or clouds, wherein many particles are lumped together so that only parcels and their collisions are tracked, and (2) the multiphase particle-in-cell, or MP-PIC, wherein the collision forces are replaced by a solids pressure term with the main purpose to avoid exceeding the maximum packing of the granular assembly. Using several cases relevant to the fluidization community, errors associated with these assumptions are computed. For these cases the magnitude of error in the time-averaged flow variables indicates that further research on the validity of these assumptions is warranted.