Efficient, scalable traffic and compressible fluid simulations using hyperbolic models

This thesis presents novel techniques for efficiently animating compressible fluids and traffic flow to improve virtual worlds. I introduce simulation methods that recreate the motion of coupled gas and elastic bodies, shockwaves in compressible gases, and traffic flows on road networks. These can all be described with mathematical models classified as hyperbolic —models with bounded speeds of information propagation. This leads to parallel computational schemes with very local access patterns. I demonstrate how these models can lead to techniques for physically plausible animations that are efficient and scalable on multi-processor architectures. Animations of gas dynamics, from curling smoke to sonic booms, are visually exciting. Existing computational models of fluids in computer graphics are unsuitable for properly describing compressible gas flows—I present a method based on a truly compressible model of gas to simulate two-way coupling between gases and elastic bodies on simplicial meshes that can handle large-scale simulation domains in a fast and scalable manner. Computational models of fluids used so far in graphics are inappropriate for describing supersonic gas dynamics because they assume the presence of smooth solutions. I present a technique for the simulation of explosive gas phenomena that addresses the challenges found in animation—namely stability, efficiency, and generality. I also demonstrate how this method is able to achieve near-linear scaling on modern many-core architectures. Automobile traffic is ubiquitous in modern life; I present a traffic animation technique that uses a hyperbolic continuum model for traffic dynamics and a discrete representation that allows visual depiction and fine control. I demonstrate how this approach outperforms agent-based models for traffic simulation. Additionally, I couple discrete agent-based vehicle simulation to continuum traffic. My hybrid technique captures the interaction between arbitrarily arranged regions of a road network and dynamically transitions between the two models. I present an analysis of the impact my hybrid technique on the ability of simulation to mimic real-world vehicle trajectory data. The methods presented in this dissertation use hyperbolic models for natural and man-made phenomena to open new possibilities for the efficient creation of physically-based animations.