Numerische Simulationen für granulare Medien

Sand is one of the least noticed but almost ubiquitous things in our environment. In physics, too, "simple" sand, or more precisely "granular media", is still a little-studied field. That this is so is due to the complexity hidden in the apparent "simplicity". An analytical solution is self-evident, because the nature of the interaction, friction processes and number of particles form an insurmountable obstacle. But even statistical physics does not yet offer any explanatory models for a pile of sand. Thus, today's knowledge about granular media consists almost exclusively of empirical values from engineers who know the angle of repose and the filling of space. Phenomena such as the processes in heaps, flow behaviour, space filling, the behaviour under vibration, avalanches and many others are known, but exact knowledge about them does not exist. The advent of digital computing systems has made it possible to simulate nature. However, until a few years ago, computing power was too low to allow the accurate study of granular media on a reasonable scale. In order to save computing time and still simulate an acceptable number of grains of sand, one was forced to accept drastic simplifications. Thus, work is almost always done in two dimensions and in some cases even the free movement is restricted by a movement on a grid. Since the most time-consuming calculation is usually that of the collision of the particles, their shape was also simplified. Usually, in the 2-dimensional, circles are used, but in the meantime also polyhedra. In the field of 3-dimensional simulations, almost only spheres or ellipsoids have been used so far. The aim of this work is to find the basis for a more realistic simulation in three dimensions. A three-dimensional simulation with convex polyhedra of as high a surface area as possible was aimed at. An increasing number of particles should not adversely affect the simulation, the runtime behaviour should be linear. Later extensions in the direction of parallelism or similar should be possible. This results in problems of various kinds. General algorithms for the calculation of the most important quantities such as volume, centre of gravity and inertia tensor for irregular polyhedra must be developed. The numerical errors in the description of rotation with matrices must be circumvented. The main problem is collision detection, as this is where most of the computing time was wasted in previous simulations.