Accurately simulating vorticity, as exemplified by the spinning motion of a flowing fluid, is an incredibly tall order even for today’s computers, says Peter Schröder, a Shaler Arthur Hanisch Professor of Computer Science and Applied and Computational Mathematics in the Division of Engineering and Applied Science.
His new technique, developed with fellow Caltech researchers and presented at the International Conference and Exhibition on Computer Graphics & Interactive Techniques (SIGGRAPH), held in Anaheim, California, from July 24-28, allows computers to simulate large-scale motion numerically using the mathematics that govern the universe at the quantum level.
“Since we are computer graphics folk, we are interested in methods that capture the visual variety and drama of fluids well. What’s unique about our method is that we took a page from the quantum mechanics’ playbook.”
In the words of Schröder’s team, writing in their paper, the resulting algorithm is “simple, unconditionally stable, and efficient”.
Richard Feynman was one of the first to recognize that superfluids (i.e., fluids cooled to temperatures near absolute zero that behave as though they have no viscosity, or resistance to gradual deformation) are governed by so-called vortex filaments, which are basically long strings of pure vorticity.
Now, with the help of a slightly tweaked Schrödinger equation, the research team was able to graphically render fluids at the macroscopic level.
“The Schrödinger equation, as we use it, is a close relative of the non-linear Schrödinger equation which is used for the description of superfluids. Their vorticity behaviour is in many ways very similar to the behaviour we can also observe in the macroscopic world.”
Schröder and his team hope their work will have an impact on computer graphics and for developing much more advanced, graphically-rendered models of real-world phenomena, such as tornadoes and hurricanes, thereby greatly enhancing the accuracy of climate modelling.
The paper, entitled “Schrödinger’s Smoke” was presented on July 26, and includes demonstrations under a variety of scenarios, comparisons with experiments, and evaluations against benchmark tests.