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Smoke Rings from Smoke

Weißmann, Steffen and Pinkall, Ulrich and Schröder, Peter (2014) Smoke Rings from Smoke. ACM Transactions on Graphics, 33 (4). Art. No. 140. ISSN 0730-0301. doi:10.1145/2601097.2601171.

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We give an algorithm which extracts vortex filaments ("smoke rings") from a given 3D velocity field. Given a filament strength h > 0, an optimal number of vortex filaments, together with their extent and placement, is given by the zero set of a complex valued function over the domain. This function is the global minimizer of a quadratic energy based on a Schrödinger operator. Computationally this amounts to finding the eigenvector belonging to the smallest eigenvalue of a Laplacian type sparse matrix. Turning traditional vector field representations of flows, for example, on a regular grid, into a corresponding set of vortex filaments is useful for visualization, analysis of measured flows, hybrid simulation methods, and sparse representations. To demonstrate our method we give examples from each of these.

Item Type:Article
Related URLs:
URLURL TypeDescription ItemProject website
Schröder, Peter0000-0002-0323-7674
Additional Information:© 2014 ACM, Inc. Publication Date: July 2014. Dan Troolin (TSI Inc.) kindly provided the velocity data used in Sec. 4.3. We thank Matthias Durynek for his support with the water vapor photograph and Albert Chern for the Matlab implementation. This work was supported in part by DFG Research Center Matheon, SFB/Transregio 109 “Discretization in Geometry and Dynamics,” and Side Effects Software.
Funding AgencyGrant Number
DFG Research Center MatheonUNSPECIFIED
SFB/Transregio 109 “Discretization in Geometry and Dynamics"UNSPECIFIED
Subject Keywords:Vortex filaments, DEC, Schrödinger operator, vortex reconnection, hairpin removal, hybrid methods, fluid simulation
Issue or Number:4
Record Number:CaltechAUTHORS:20140820-105147740
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Official Citation:Smoke rings from smoke Steffen Weißmann, Ulrich Pinkall, Peter Schröder Article No.: 140 doi>10.1145/2601097.2601171
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:48725
Deposited By: Ruth Sustaita
Deposited On:20 Aug 2014 20:10
Last Modified:10 Nov 2021 18:34

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