Reservoir computing model of two-dimensional turbulent convection

Pandey, Sandeep; Schumacher, Jörg

doi:10.48550/arxiv.2001.10280

Cited by 2 publications

(3 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, the continuation of the optimal scaling with β 0.3 begs the question as to whether or not the transition in 2D exponent at Ra = 10 13 [38] could be related to boundary-layer structures with horizontal and vertical scales determined by the optimal solution. Thus, it would undoubtedly be revealing to pursue higher values of Ra in 2D, along with application of other types of data analyses ( [29,60,[82][83][84][85]), in the exploration of exact coherent solutions.…”

Section: Discussionmentioning

confidence: 99%

Coherent Solutions and Transition to Turbulence in Two-Dimensional Rayleigh-Bénard Convection

Kooloth,

Sondak,

Smith

2020

Preprint

View full text Add to dashboard Cite

For two-dimensional (2D) Rayleigh-Bénard convection, classes of unstable, steady solutions were previously computed using numerical continuation [1,2]. The 'primary' steady solution bifurcates from the conduction state at Ra ≈ 1708, and has a characteristic aspect ratio (length/height) of approximately 2. The primary solution corresponds to one pair of counterclockwise-clockwise convection rolls with a temperature updraft in between and an adjacent downdraft on the sides. By adjusting the horizontal length of the domain, [1, 2] also found steady, maximal heat transport solutions, with characteristic aspect ratio less than 2 and decreasing with increasing Ra. Compared to the primary solutions, optimal heat transport solutions have modifications to boundary layer thickness, the horizontal length scale of the plume, and the structure of the downdrafts. The current study establishes a direct link between these (unstable) steady solutions and transition to turbulence for P r = 7 and P r = 100. For transitional values of Ra, the primary and optimal-heattransport solutions both appear prominently in appropriately-sized sub-fields of the time-evolving temperature fields. For Ra beyond transitional, our data analysis shows persistence of the primary solution for P r = 7, while the optimal heat transport solutions are more easily detectable for P r = 100. In both cases P r = 7 and P r = 100, the relative prevalence of primary and optimal solutions is consistent with the N u vs. Ra scalings for the numerical data and the steady solutions.

show abstract

Section: Discussionmentioning

confidence: 99%

Coherent Solutions and Transition to Turbulence in Two-Dimensional Rayleigh-Bénard Convection

Kooloth,

Sondak,

Smith

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…On the contrary, it can be seen that the original PINN approach miss a large part of the warm plumes, but especially the cold (descending) ones. Figures (12) were chosen to show an example on how the surrogate is capable of accurately predicting a strong small plume with very anisotropic structure, despite being located close to the domain boundaries and occurring at a time instant never visited during training. It is remarkable how well the intricate temperature distribution within the plume is approached by PINN r .…”

Section: Improving Modeling Capability For More Turbulent Scenario By...mentioning

confidence: 99%

“…Pandey et al were more interested by turbulent statistical prediction of 2D large scale structures. They relied on reservoir computing modeling, which may be seen as an hybridization between a proper orthogonal decomposition (POD) of DNS data and a recurrent neural network (RNN), to tackle RB cavity flow at Ra = 10 7 [12]. At the foundation of all of these works is the use of large DNS database from which partial information, in the form of wall data or time-windowed averaging, or more global information, in the form of POD, are extracted.…”

Section: Introductionmentioning

confidence: 99%

Physics-aware deep neural networks for surrogate modeling of turbulent natural convection

Lucor,

Agrawal,

Sergent

2021

Preprint

View full text Add to dashboard Cite

Recent works have explored the potential of machine learning as data-driven turbulence closures for RANS and LES techniques. Beyond these advances, the high expressivity and agility of physics-informed neural networks (PINNs) make them promising candidates for full fluid flow PDE modeling. An important question is whether this new paradigm, exempt from the traditional notion of discretization of the underlying operators very much connected to the flow scales resolution, is capable of sustaining high levels of turbulence characterized by multi-scale features? We investigate the use of PINNs surrogate modeling for turbulent Rayleigh-Bénard (RB) convection flows in rough and smooth rectangular cavities, mainly relying on DNS temperature data from the fluid bulk. We carefully quantify the computational requirements under which the formulation is capable of accurately recovering the flow hidden quantities. We then propose a new padding technique to distribute some of the scattered coordinates -at which PDE residuals are minimized -around the region of labeled data acquisition. We show how it comes to play as a regularization close to the training boundaries which are zones of poor accuracy for standard PINNs and results in a noticeable global accuracy improvement at iso-budget. Finally, we propose for the first time to relax the incompressibility condition in such a way that it drastically benefits the optimization search and results in a much improved convergence of the composite loss function. The RB results obtained at high Rayleigh number Ra = 2 • 10 9 are particularly impressive: the predictive accuracy of the surrogate over the entire half a billion DNS coordinates yields errors for all flow variables ranging between [0.3% − 4%] in the relative L 2 norm, with a training relying only on 1.6% of the DNS data points.

show abstract

Reservoir computing model of two-dimensional turbulent convection

Cited by 2 publications

References 39 publications

Coherent Solutions and Transition to Turbulence in Two-Dimensional Rayleigh-Bénard Convection

Coherent Solutions and Transition to Turbulence in Two-Dimensional Rayleigh-Bénard Convection

Physics-aware deep neural networks for surrogate modeling of turbulent natural convection

Contact Info

Product

Resources

About