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Inside fluids: clebsch maps for visualization and processing

Published: 20 July 2017 Publication History

Abstract

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.

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cover image ACM Transactions on Graphics
ACM Transactions on Graphics  Volume 36, Issue 4
August 2017
2155 pages
ISSN:0730-0301
EISSN:1557-7368
DOI:10.1145/3072959
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 20 July 2017
Published in TOG Volume 36, Issue 4

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Author Tags

  1. analysis
  2. clebsch maps
  3. enhancement
  4. flow visualization
  5. fluid dynamics

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