The natural Helmholtz-Hodge decomposition for open-boundary flow analysis

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Publication Type pre-print
School or College <blank>
Department Computing, School of
Creator Pascucci, Valerio
Other Author Bhatia, Harsh; Bremer, Peer-Timo
Title The natural Helmholtz-Hodge decomposition for open-boundary flow analysis
Date 2014-01-01
Description The Helmholtz-Hodge decomposition (HHD), which describes a flow as the sum of an incompressible, an irrotational, and a harmonic flow, is a fundamental tool for simulation and analysis. Unfortunately, for bounded domains, the HHD is not uniquely defined, traditionally, boundary conditions are imposed to obtain a unique solution. However, in general, the boundary conditions used during the simulation may not be known known, or the simulation may use open boundary conditions. In these cases, the flow imposed by traditional boundary conditions may not be compatible with the given data, which leads to sometimes drastic artifacts and distortions in all three components, hence producing unphysical results. This paper proposes the natural HHD, which is defined by separating the flow into internal and external components. Using a completely data-driven approach, the proposed technique obtains uniqueness without assuming boundary conditions a priori. As a result, it enables a reliable and artifact-free analysis for flows with open boundaries or unknown boundary conditions. Furthermore, our approach computes the HHD on a point-wise basis in contrast to the existing global techniques, and thus supports computing inexpensive local approximations for any subset of the domain. Finally, the technique is easy to implement for a variety of spatial discretizations and interpolated fields in both two and three dimensions.
Type Text
Publisher Institute of Electrical and Electronics Engineers (IEEE)
Volume 20
Issue 11
First Page 1566
Last Page 1578
Language eng
Bibliographic Citation Bhatia, H., Pascucci, V., & Bremer, P.-T. (2014). The natural Helmholtz-Hodge decomposition for open-boundary flow analysis. IEEE Transactions on Visualization and Computer Graphics, 20(11), 1566-78.
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Identifier uspace,19013
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Date Created 2014-11-14
Date Modified 2021-05-06
ID 712717
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