Parallel local time stepping for rigid bodies represented by triangulated meshes

Abstract

Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles, suffer from very stiff differential equations plus multiscale challenges in space and time. The particles move smoothly through space until they interact almost instantaneously due to collisions. Dense particle packings hence require tiny time step sizes, while free particles can advance with large time steps. Admissible time step sizes can span multiple orders of magnitudes. We propose an adaptive local time stepping algorithm which identifies clusters of particles that can be updated independently, advances them optimistically and independently in time, determines collision time stamps in space-time such that we maximise the time step sizes used, and resolves the momentum exchange implicitly. It is combined with various acceleration techniques which exploit multiscale geometry representations and multiscale behaviour in time. The collision time stamp detection in space-time in combination with the implicit solve of the actual collision equations avoids that particles get locked into tiny time step sizes, the clustering yields a high concurrency level, and the acceleration techniques plus local time stepping avoid unnecessary computations. This brings a scaling, adaptive time stepping for DEM for real-world challenges into reach.