Computer simulations of granular materials based on the distinct element method (DEM) are now commonly used in the design and optimization of industrial processes. One of the leading mathematical approach to DEM uses dynamic triangulations for detecting collisions among moving spheres, and relies on advanced data structures and on the exact numerical evaluation of computational geometry predicates. This paper outlines the simulation method and introduces the robust and adaptive computation of predicates using standard floating point operations. Finally, some application examples are shown.