Albert Chern: Schrödinger’s Smoke

Abstract:

Simulation of incompressible fluids has been a challenging numerical task in computer graphics as well as in many areas of science. We describe a new approach for the purely grid based simulation of incompressible fluids. In it, the fluid state is represented by a wave function evolving under the Schrödinger equation subject to incompressibility constraints. The underlying dynamics satisfies the Euler equation modified with a Landau-Lifshitz term. The latter ensures that dynamics due to thin vortical structures are faithfully reproduced. This enables robust simulation of intricate phenomena such as vortical wakes and interacting vortex filaments, even on modestly sized grids. The numerical algorithms for time evolution are exceedingly simple.  In the talk I will also discuss the underlying theory which reveals fascinating connections between classical fluids, quantum mechanics, super fluids, Landau-Lifshitz theory of ferromagnetic material, and the geometry of the 3-hypersphere.