  The direct numerical simulation of particulate systems offers a unique
approach to study the dynamics of fluid-solid suspensions by fully resolving
the submerged particles and without introducing empirical models. For the
lattice Boltzmann method, different variants exist to incorporate the
fluid-particle interaction into the simulation. This paper provides a detailed
and systematic comparison of two different methods, namely the momentum
exchange method and the partially saturated cells method by Noble and
Torczynski. Three subvariants of each method are used in the benchmark scenario
of a single heavy sphere settling in ambient fluid to study their
characteristics and accuracy for particle Reynolds numbers from 185 up to 365.
The sphere must be resolved with at least 24 computational cells per diameter
to achieve velocity errors below 5%. The momentum exchange method is found to
be more accurate in predicting the streamwise velocity component whereas the
partially saturated cells method is more accurate in the spanwise components.
The study reveals that the resolution should be chosen with respect to the
coupling dynamics, and not only based on the flow properties, to avoid large
errors in the fluid-particle interaction.
