Protons and heavy-ion beams at unprecedented energies are brought into collisions in the CERN Large Hadron Collider (LHC) for high-energy experiments. The LHC multistage collimation system is designed to provide protection against regular and abnormal losses in order to reduce the risk of quenches of the superconducting magnets as well as keeping background in the experiments under control. Compared to protons, beam collimation in the heavy-ion runs is more challenging despite the lower stored beam energies, because the efficiency of cleaning with heavy ions has been observed to be 2 orders of magnitude worse. This is due to the differences in the interaction mechanisms between the beams and the collimators. Ion beams experience fragmentation and electromagnetic dissociation at the collimators that result in a substantial flux of off-rigidity particles that escape the collimation system. These out-scattered nuclei might be lost around the ring, eventually imposing a limit on the maximum achievable stored beam energy. The more stringent limit comes from potential quenches of superconducting magnets. Accurate simulation tools are crucial in order to understand and control these losses. A new simulation framework has been developed for heavy-ion collimation based on the coupling of the SixTrack tracking code, which has been extended to track arbitrary heavy-ion species, and the fluka Monte Carlo code that models the electromagnetic and nuclear interactions of the heavy ions with the nuclei of the collimator material. In this paper, the functionality of the new simulation tool is described. Furthermore, SixTrack-fluka coupling simulations are presented and compared with measurements done with 208 Pb 82+ ions in the LHC. The agreement between simulations and measurements is discussed and the results are used to understand and optimize losses. The simulation tool is also applied to predict the performance of the collimation system for the high-luminosity LHC. Based on the simulation results and the experience gained in past heavy-ion runs, some conclusions are presented.