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Inside Fluids: Clebsch Maps for Visualization and Processing

Chern, Albert and Knöppel, Felix and Pinkall, Ulrich and Schröder, Peter (2017) Inside Fluids: Clebsch Maps for Visualization and Processing. ACM Transactions on Graphics, 36 (4). Art No. 142. ISSN 0730-0301. doi:10.1145/3072959.3073591.

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Clebsch maps encode velocity fields through functions. These functions contain valuable information about the velocity field. For example, closed integral curves of the associated vorticity field are level lines of the vorticity Clebsch map. This makes Clebsch maps useful for visualization and fluid dynamics analysis. Additionally they can be used in the context of simulations to enhance flows through the introduction of subgrid vorticity. In this paper we study spherical Clebsch maps, which are particularly attractive. Elucidating their geometric structure, we show that such maps can be found as minimizers of a non-linear Dirichlet energy. To illustrate our approach we use a number of benchmark problems and apply it to numerically given flow fields. Code and a video can be found in the ACM Digital Library.

Item Type:Article
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Schröder, Peter0000-0002-0323-7674
Alternate Title:Inside fluids
Additional Information:© 2017 ACM. This work was supported in part by the DFG Collaborative Research Center TRR 109 “Discretization in Geometry and Dynamics.” Additional support was provided by SideFX software. The Bunny model is courtesy Stanford Computer Graphics laboratory.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)TRR 109
Issue or Number:4
Record Number:CaltechAUTHORS:20170814-144752570
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Official Citation:Albert Chern, Felix Knöppel, Ulrich Pinkall, and Peter Schröder. 2017. Inside fluids: clebsch maps for visualization and processing. ACM Trans. Graph. 36, 4, Article 142 (July 2017), 11 pages. DOI:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80377
Deposited On:14 Aug 2017 22:13
Last Modified:15 Nov 2021 19:30

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