Topological Analysis of High Velocity Turbulent Flow

Bridel-Bertomeu, Thibault; Fovet, Benjamin; Tierny, Julien; Vivodtzev, Fabien

doi:10.1109/ldav48142.2019.8944351

Cited by 6 publications

(3 citation statements)

References 12 publications

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“…Such a transition to a scalar descriptor enables them to leverage the existing tools for scalar data analysis. For instance, several authors [18,60] have shown that, given a relevant vorticity scalar descriptor, the center of the flow vortices could be reliably extracted and tracked over time, which supports the idea that topological methods for scalar data can be useful for the description of specific flow features. Thus, in the following, we describe the literature related to topological methods for scalar data.…”

Section: Related Workmentioning

confidence: 69%

“…Moreover, the utility of TDA has been already demonstrated in a number of analysis and visualization tasks [51], with examples of successful applications in combustion [16,43,68], material sciences [33,45,46], bioimaging [2,12,21], quantum chemistry [9,39,82], or astrophysics [101,102]. In particular, the critical points of flow vorticity indicators have been reported to appropriately capture the center of vortices [18,60], as well as their importance, with the notion of topological persistence [30]. Such results provide additional evidence and consolidate the intuition that TDA could be a relevant framework for comparing turbulent flows.…”

Section: Introductionmentioning

confidence: 99%

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Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows -- An Experimental Study

Nauleau¹,

Vivodtzev²,

Bridel-Bertomeu³

et al. 2022

Preprint

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1: Topological Data Analysis protocols applied on an ensemble dataset of a Kelvin-Helmholtz instability. (a) The 180 members of the ensemble obtained with variations of timesteps, interpolation schemes, orders, resolutions and Riemann solvers (Tab. 1). (b)The top cluster represents the time separation of t 0 and t 1 for the flows S 1 and S 2 with the Wasserstein distance and the bottom cluster with the L 2 -norm. Red lines show the timestep separation with our clustering method whereas the sphere colors are the ground truth, illustrating the limitation of the L 2 -norm. (c) Persistence curve protocol: Differences between integrals of persistence curves (gray area) of the enstrophy computed with a SLAU2 solver, an order 7 TENO scheme and a resolution of 1024 × 1024 for various configurations (S 1 at t 0 , S 2 and S 3 at t 1 ). These integral differences exhibit the appearance of vortices (critical points) as the time increases. (d) Outlier distance protocol: Wasserstein distance matrix for 5 configurations S 1 (t 0 , HLLC), S 2 (t 1 , Roe), S 3 (t 1 , HLLC), S 4 (t 2 , Roe), S 5 (t 2 , HLLC) computed with an order 7 WENO-Z interpolation scheme at 512 × 512. The sum of each row the configuration maximizing this distance between solvers and timesteps, here S 1 . (e) Unsupervised classification: Wasserstein distance matrix for the previous configurations with an order 7 WENO-Z interpolation scheme at 256 × 256. The clustering based on the Wasserstein distance and colored according to the Kmeans clustering method successfully segments the time steps.

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Section: Related Workmentioning

confidence: 69%

Section: Introductionmentioning

confidence: 99%

Topological Analysis of Ensembles of Hydrodynamic Turbulent Flows -- An Experimental Study

Nauleau¹,

Vivodtzev²,

Bridel-Bertomeu³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Topological data analysis of the O Ba scalar function. Motivated by the success of TDA to describe scalar data through its topological features in numerous applications [9][10][11][12][13][14] including vortex extraction, 15,16 we apply TDA tools to the O Ba scalar field. To our best knowledge, it is the first report on employing TDA in the MICD context.…”

Section: Introductionmentioning

confidence: 99%