ITR: Tools For High-Performance Simulation of Granular Materials

University Of Iowa, Iowa City IA

Investigators

Abstract

This grant is for the development of computational tools for simulating very large-scale problems involving granular flow. Rather than use a continuum model of a granular material (which involves a large number of assumptions and approximations about the way they behave), rather we look at the computational challenges in discrete element models. These are challenging large-scale problems with thousands to millions of grains that have to be simulated. Direct interactions are usually between touching grains. However, one grain can not only affect the others that it touches, but those will affect their neighbors, and so on. Further, the network of interactions is dynamic. Indeed, the overall pattern of interactions can become very different depending on the circumstances: if a sand table is shaken, then most of the sand grains will be independent; when the grains settle, each grain will be touching many others. In order to efficiently organize the computational tasks, we need to use techniques from graph or network theory. These tools include graph partitioning techniques, graph coloring techniques, and new techniques for handling the collisions of grains. Since the problems are very large scale, currently available techniques often have to be adapted from dealing with small-scale problems to deal with large-scale problems. Furthermore, since the network of interactions is dynamic, these techniques have to be adapted to use information about the previous network in order to efficiently obtain the corresponding information about the new network. In this project, we will be developing these tools and drawing techniques from graph theory, continuous optimization, complementarity theory, and computational geometry. Granular materials are materials made of small, relatively hard objects that collide off each other. Sand, breakfast cereals, talcum powder, and a box of marbles are all examples of granular materials. Understanding these materials and simulating their behavior directly is difficult because the position and velocity of each of the ``grains'' in the material needs to be tracked and updated as they move and collide. In order to do this well, we need high-performance computers, and we need to use them well. The crucial problem is to understand the nature of the interactions between the grains, and to develop automatic tools that can determine how to divide the computational tasks so that they can be tackled efficiently on high-performance and parallel computers.