Simulating Granular Materials Using a 3D Voronoi Subdivision Tree

Abstract:

Our world is full of many different types of granular materials. This includes materials such as silt, sand, and gravel and have various sizes and properties. It is of interest to simulate and visualize granular media as it can provide additional analysis and insight into geologic events such as landslides or debris flows. Unfortunately, this can be a computationally complex problem due to the large amount of physical interaction between granular materials. To help alleviate this problem, we have developed a method to represent granular media using a technique called a 3D Voronoi Subdivision Tree. The idea behind our method is to take a convex terrain volume and use a subdivision tree to build smaller, granular subpieces contained within the volume. We use a 3D Voronoi subdivision technique to create smaller granular convex cells and then store them in the tree. The tree is dynamic and adaptive as it only represents individual granular media when they are needed. In addition, as each of the granular subpieces are created, we can also store attributes of that granular material in the tree node. This ensures a diversity of granular materials contained within the volume. In order to maintain performance during simulation, we can dynamically replace parts of the granular volume with smaller granular subpieces just by traversing the tree. In essence, this allows for many different granular materials to be represented within the volume while reducing computational complexity. As such, this helps with simulation performance so that focus can be placed on simulation analysis. We feel our method is helpful for simulating geologic events with granular materials and will assist geoscientists in understanding them.