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Schrödinger's smoke

Published: 11 July 2016 Publication History

Abstract

We describe a new approach for the purely Eulerian simulation of incompressible fluids. In it, the fluid state is represented by a C2-valued wave function evolving under the Schrödinger equation subject to incompressibility constraints. The underlying dynamical system is Hamiltonian and governed by the kinetic energy of the fluid together with an energy of Landau-Lifshitz type. The latter ensures that dynamics due to thin vortical structures, all important for visual simulation, are faithfully reproduced. This enables robust simulation of intricate phenomena such as vortical wakes and interacting vortex filaments, even on modestly sized grids. Our implementation uses a simple splitting method for time integration, employing the FFT for Schrödinger evolution as well as constraint projection. Using a standard penalty method we also allow arbitrary obstacles. The resulting algorithm is simple, unconditionally stable, and efficient. In particular it does not require any Lagrangian techniques for advection or to counteract the loss of vorticity. We demonstrate its use in a variety of scenarios, compare it with experiments, and evaluate it against benchmark tests. A full implementation is included in the ancillary materials.

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cover image ACM Transactions on Graphics
ACM Transactions on Graphics  Volume 35, Issue 4
July 2016
1396 pages
ISSN:0730-0301
EISSN:1557-7368
DOI:10.1145/2897824
Issue’s Table of Contents
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Publication History

Published: 11 July 2016
Published in TOG Volume 35, Issue 4

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Author Tags

  1. Schrödinger operator
  2. discrete differential geometry
  3. fluid simulation

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