A Caltech Library Service

Schrödinger's smoke

Chern, Albert and Knöppel, Felix and Pinkall, Ulrich and Schröder, Peter and Weißmann, Steffen (2016) Schrödinger's smoke. ACM Transactions on Graphics (TOG), 35 (4). Art. No. 77. ISSN 0730-0301. doi:10.1145/2897824.2925868.

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item:


We describe a new approach for the purely Eulerian simulation of incompressible fluids. In it, the fluid state is represented by a C^2-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.

Item Type:Article
Related URLs:
URLURL TypeDescription
Schröder, Peter0000-0002-0323-7674
Additional Information:© 2016 ACM. This work was supported in part by the DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics,” Joel A. Tropp under the auspices of ONR grant N00014-11-1-0025, and the German Academic Exchange Service (DAAD). Additional support was provided by IST at Caltech, SideFX software, and Framestore Los Angeles. We also gratefully acknowledge Alessandro Pepe’s help with visualization. The Bunny model is courtesy Stanford Computer Graphics laboratory while the Teapot is courtesy the Computer Graphics program at the University of Utah.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)TRR 109
Office of Naval Research (ONR)N00014-11-1-0025
Deutscher Akademischer Austauschdienst (DAAD)UNSPECIFIED
Subject Keywords:discrete differential geometry, fluid simulation, Schrödinger operator, Mathematics of computing → Partial differential equations; Computing methodologies → Physical simulation; Applied computing → Physics
Issue or Number:4
Record Number:CaltechAUTHORS:20160727-095740856
Persistent URL:
Official Citation:Albert Chern, Felix Knöppel, Ulrich Pinkall, Peter Schröder, and Steffen Weißmann. 2016. Schrödinger's smoke. ACM Trans. Graph. 35, 4, Article 77 (July 2016), 13 pages. DOI:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69242
Deposited On:27 Jul 2016 17:09
Last Modified:11 Nov 2021 04:11

Repository Staff Only: item control page