An implementation of viscous pressure-force (‘soft-sphere’) model in REBOUND for local ring simulations

Abstract

ABSTRACT Numerical simulations are an essential tool for studying dynamics of dense, self-gravitating planetary rings. Here, we present a new implementation of a soft-sphere collision model into the parallel gravitational N-body code REBOUND. Specifically, our module is designed for simulations done in the local shearing sheet approximation, and includes a simple viscoelastic model for the contact forces between colliding particles. The soft-sphere treatment is particularly important in regimes where collisions cannot be treated as independent binary impacts, as is done in the hard-sphere method already implemented in the code. The new module is fully parallelized with MPI and it can be used in conjunction with the available gravity octree method, also fully parallelized, to perform self-gravitating simulations. We check the validity of our soft-sphere model by successfully reproducing the main steady-state properties of non-gravitating and self-gravitating systems reported in earlier literature. Moreover, we show that it gives realistic results also in the high optical depth and strong self-gravity regimes, where the hard-sphere method fails due to particle overlaps. In addition, we test the CPU-scaling and efficiency of the MPI-parallelization. The algorithm proves to retain much of the original REBOUND speed without sacrificing the accuracy of the results. Our new tool can thus be applied with confidence to planetary ring studies, such as those aimed at understanding the onset and evolution of viscous overstability in dense self-gravitating rings.