Tensor-based flow reconstruction from optimally located sensor measurements

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...

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Bibliographic Details
Published in:Journal of fluid mechanics 2023-05, Vol.962, Article A27
Main Authors: Farazmand, Mohammad, Saibaba, Arvind K.
Format: Article
Language:English
Subjects:
Computational efficiency
Computer applications
Computing costs
Dimensions
Flow simulation
Fluid dynamics
Hydrodynamics
JFM Papers
Libraries
Linear algebra
Marine sciences
Mathematical analysis
Mechanics
Methods
Neural networks
Physics
Reconstruction
Research vessels
Sea surface
Sea surface temperature
Sensors
Simulation
Sparsity
Storage requirements
Surface temperature
Tensors
Three dimensional flow
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Summary: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 situ and satellite measurements of the global sea surface temperature and three-dimensional unsteady simulated flow around a marine research vessel.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2023.269