  The simulation of geometrically resolved rigid particles in a fluid relies on
coupling algorithms to transfer momentum both ways between the particles and
the fluid. In this article, the fluid flow is modeled with a parallel Lattice
Boltzmann method using adaptive grid refinement to improve numerical
efficiency. The coupling with the particles is realized with the momentum
exchange method. When implemented in plain form, instabilities may arise in the
coupling when the particles are lighter than the fluid. The algorithm can be
stabilized with a virtual mass correction specifically developed for the
Lattice Boltzmann method. The method is analyzed for a wide set of physically
relevant regimes, varying independently the body-to-fluid density ratio and the
relative magnitude of inertial and viscous effects. These studies of a single
rising particle exhibit periodic regimes of particle motion as well as chaotic
behavior, as previously reported in the literature. The new method is carefully
compared with available experimental and numerical results. This serves to
validate the presented new coupled Lattice Boltzmann method and additionally it
leads to new physical insight for some of the parameter settings.
