Efficient and Accurate Collision Detection for Granular Flow Simulation

In this paper, we present efficient algorithms for contact detection and accurate contact mechanics in granular flow simulations. The contact detection algorithms that we present are applicable to arbitrarily shaped rigid particles in a variety of environments including interactive as well as non-interactive. We present a very accurate force displacement model for characterizing the behavior of particles in contact. These algorithms are applied to granular flow simulations, in particular, soybean flow through an inclined chute. There are two phases of this research, namely, the development of contact detection algorithms and the development of accurate contact mechanics based force-displacement models. In the first phase, the algorithms consist of two stages. The first stage involves finding candidate particles for possible contacts. The second stage involves detecting precise contact between these candidates. In our application, the soybeans, which are approximately ellipsoidal in shape, are well approximated by a cluster of overlapping spheres. Detecting precise contact between spherical shapes is quite simple and hence, in this paper, we will focus only on the first stage of the first phase. The primary data structure used in the first stage is an octree. We build an octree for the enclosure/chute (containing thenparticles) and use it in the algorithm for detecting possible contacts. The average time complexity of this stage of the first phase isO(n)and the worst case isO(nlogn). In phase two, we develop a very accurate force-displacement model for dealing with the contact mechanics of soybean flow through an inclined chute. This model is a reasonably close approximation to the widely accepted Mindlin force-displacement model for elastic frictional contacts. Our force-displacement model accounts for normal and tangential direction contact forces acting between particles and/or particles and the chute walls. We also present examples of soybean flow simulations with fast contact detection and accurate contact mechanics.