Pairwise Adaptive Timesteps for Soft-Sphere Collisions in Ring Simulations

This paper looks at integrating soft-sphere collisions using a pair-wise adaptive time step approach. One of the challenges of soft-sphere collisions, compared to hard-sphere collisions, is that a smaller time step must be used to ensure that interactions are properly integrated. As wall-clock time scales as 1/ Δt, this can be prohibitively expensive. In this paper, we examine the feasibility of using a pair-wise adaptive time step for integrating collisions both to improve the accuracy and the speed of these calculations. The implementation accuracy is tested in small runs of two or three particles, while performance tests use large configurations that mimic local-cell planetary ring simulations. We find the approach to be remarkably successful in both areas. Using an adaptive time step allows us to accurately integrate collisions across a broad range of particle sizes and impact velocities. It also gives a significant speed improvement over a fixed time step using a time step that is small enough to be reasonably accurate.