Computational models and tools for fluid animation

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Over the last decade, computer simulations of the physics of liquids and gases have come to play a critical role in the visual effects of both live-action and animated films, from Avatar to Ratatouille, by automating the creation of virtual waves, honey, explosions, fire, clouds, and more. This new toolset offers directors the ability to tell creative stories that would otherwise be prohibitively expensive, dangerous, or utterly impossible to film. Furthermore, modern computer games are beginning to incorporate fluid dynamics into their gameplay. There has also been an increasing focus on matching both analytical and experimental results, such that future interactive applications in training, education, architecture, design, and engineering are all likely to benefit from integrating fast yet accurate physics. However, this requires more than simply accelerating existing engineering methods. There remain to be solved many fundamental research questions which lie at the intersection of computer science, physics, and mathematics, and the field of computer animation offers an ideal testing ground for the pursuit of radically new solutions. Innovations in these areas also have tremendous potential for positive economic impact: the film and games industries each contribute tens of billions to the North American economy alone. Ontario-based companies dominate the world market for 3D animation software (Houdini, Autodesk), and the annual revenue of Ontario's rapidly growing computer gaming industry has been estimated to exceed $1 billion.The successes achieved to date have also served to highlight the many ways in which our current simulation tools remain inadequate, as professional visual effects artists demand the ability to simulate more detailed, more dramatic, and more complex scenarios than ever before, in less time. The focus of this research is to develop new physical models, numerical techniques, and geometric and algorithmic tools that will enable them to do so. For example, detailed simulation of water droplets requires a precise balance between strong surface tension, gravity, and fluid pressure; current numerical methods struggle to achieve this balance, yielding unfortunate visible errors as a result. Accurately representing the evolution of rapidly deforming liquid surfaces is an ongoing challenge, particularly for foams, bubbles, and complex multiphase liquid mixtures (e.g. oil/water/air). Very thin liquid sheets and jets which arise during splashing currently consume massive computational resources with existing methods. This research proposal will tackle these problems, leveraging our established expertise with embedded boundary methods, triangle meshes with dynamic topology, and modeling techniques for reduced dimensional objects.These advances will most immediately impact computer animation and visual effects, increasing the power and productivity of software tools used by technical artists. At the same time, the fundamental computational tools we aim to develop will ultimately have wide applicability across the sciences, from material scientists studying the evolution of foams and grains, to future surgeons training on simulated virtual humans whose hearts pump simulated blood. Within the field of computer graphics, this work will contribute fundamentally to our understanding of how best to represent and manipulate the discrete geometry, topology, and physics of both fluids and fluid-like materials which undergo large and dramatic deformations.