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Tensor-based flow reconstruction from optimally located sensor measurements

Journal Article · · Journal of Fluid Mechanics
DOI:https://doi.org/10.1017/jfm.2023.269· OSTI ID:2422209

Reconstructing high-resolution flow fields from sparse measurements is a major challenge in fluid dynamics. Existing methods often vectorize the flow by stacking different spatial directions on top of each other, hence confounding the information encoded in different dimensions. Here, we introduce a tensor-based sensor placement and flow reconstruction method which retains and exploits the inherent multidimensionality of the flow. We derive estimates for the flow reconstruction error, storage requirements and computational cost of our method. We show, with examples, that our tensor-based method is significantly more accurate than similar vectorized methods. Furthermore, the variance of the error is smaller when using our tensor-based method. While the computational cost of our method is comparable to similar vectorized methods, it reduces the storage cost by several orders of magnitude. The reduced storage cost becomes even more pronounced as the dimension of the flow increases. We demonstrate the efficacy of our method on three examples: a chaotic Kolmogorov flow,in situand satellite measurements of the global sea surface temperature and three-dimensional unsteady simulated flow around a marine research vessel.

Research Organization:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
SC0023188
OSTI ID:
2422209
Journal Information:
Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 962; ISSN 0022-1120
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English

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