Towards a Framework for the Stochastic Modelling of Subgrid Scale Fluxes for Large Eddy Simulation

Larcher, Thomas von; Beck, Andrea; Klein, Rupert; Horenko, Illia; Metzner, Philipp; Waidmann, Matthias; Igdalov, Dimitri; Gassner, Gregor J.; Munz, Claus‐Dieter

doi:10.1127/metz/2015/0581

Cited by 4 publications

(5 citation statements)

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“…The direct prediction of the closure terms instead of their modeling offers an alternative to the parameter estimation task in the previous section. Here, the unknown terms in Equation () are directly approximated by the ML algorithm—either as fluxes or as the forces themselves [5,21,79‐81,84,86,90]. Important to stress, however, is that the mapping from the coarse to the fine field is nonunique, and thus, each coarse field is associated with a distribution of corresponding closure terms.…”

Section: Examples Of Ml‐augmented Turbulence Modelingmentioning

confidence: 99%

“…In an a posteriori application of the subgrid force together with a dissipative regularization term, the approach outperforms classical closure models. In [81], the authors applied a method for a stochastic model discrimination based on autoregressive models with external influences on the reconstruction of subfilter fluxes in finite‐volume LES. Here, the model was not only able to capture the time‐space structure of the subgrid fluxes reliably but also identify flow regimes, for example, the near‐wall region in a turbulent boundary layer, that require their own local model (an example of an unsupervised clustering method).…”

Section: Examples Of Ml‐augmented Turbulence Modelingmentioning

confidence: 99%

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A perspective on machine learning methods in turbulence modeling

Beck

Kurz

2021

GAMM-Mitteilungen

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This work presents a review of the current state of research in data‐driven turbulence closure modeling. It offers a perspective on the challenges and open issues but also on the advantages and promises of machine learning (ML) methods applied to parameter estimation, model identification, closure term reconstruction, and beyond, mostly from the perspective of large Eddy simulation and related techniques. We stress that consistency of the training data, the model, the underlying physics, and the discretization is a key issue that needs to be considered for a successful ML‐augmented modeling strategy. In order to make the discussion useful for non‐experts in either field, we introduce both the modeling problem in turbulence as well as the prominent ML paradigms and methods in a concise and self‐consistent manner. In this study, we present a survey of the current data‐driven model concepts and methods, highlight important developments, and put them into the context of the discussed challenges.

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Section: Examples Of Ml‐augmented Turbulence Modelingmentioning

confidence: 99%

Section: Examples Of Ml‐augmented Turbulence Modelingmentioning

confidence: 99%

A perspective on machine learning methods in turbulence modeling

Beck

Kurz

2021

GAMM-Mitteilungen

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“…Here, the unknown terms in Eq. 6 are directly approximated by the ML algorithm -either as fluxes or as the forces themselves [69,68,67,4,75,73,16,78]. Important to stress however is the ambiguity of coarse to fine field, and thus of the coarse field to the closure terms.…”

Section: Closure Term Estimationmentioning

confidence: 99%

“…In an a posteriori application of the subgrid force together with a dissipative regularization term their approach outperforms classical closure models. In [69], the authors applied a method for a stochastic model-discrimination based on so-called vector-valued auto-regressive models with external influences to the reconstruction of subfilter fluxes in Finite-Volume LES. Here, the model was not only able to capture the time-space structure of the subgrid fluxes reliably, but also to identify flow regimes, for example the near-wall region in a turbulent boundary layer that require their own local model (an example of an unsupervised clustering method).…”

Section: Closure Term Estimationmentioning

confidence: 99%

A Perspective on Machine Learning Methods in Turbulence Modelling

Beck¹,

Kurz²

2020

Preprint

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This work presents a review of the current state of research in data-driven turbulence closure modeling. It offers a perspective on the challenges and open issues, but also on the advantages and promises of machine learning methods applied to parameter estimation, model identification, closure term reconstruction and beyond, mostly from the perspective of Large Eddy Simulation and related techniques. We stress that consistency of the training data, the model, the underlying physics and the discretization is a key issue that needs to be considered for a successful ML-augmented modeling strategy. In order to make the discussion useful for non-experts in either field, we introduce both the modeling problem in turbulence as well as the prominent ML paradigms and methods in a concise and self-consistent manner. Following, we present a survey of the current data-driven model concepts and methods, highlight important developments and put them into the context of the discussed challenges.

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“…Here, we make not use of data of the original grid but of the so-called fine grid that is 600 × 352 × 600 in (x,y,z), and we have applied a post-processing procedure to obtain a constant grid increment throughout the y-direction instead of the polynomial distribution of the original grid. We refer to [22] for a detailed description of the postprocessing algorithms that convert the original data to the equidistant fine grid data.…”

Section: Channel Turbulence Flowmentioning

confidence: 99%

On identification of self-similar characteristics using the Tensor Train decomposition method with application to channel turbulence flow

Larcher¹,

Klein

2019

Theor. Comput. Fluid Dyn.

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A study on the application of the Tensor Train decomposition method to 3D direct numerical simulation data of channel turbulence flow is presented. The approach is validated with respect to compression rate and storage requirement. In tests with synthetic data, it is found that grid-aligned self-similar patterns are well captured, and also the application to non grid-aligned self-similarity yields satisfying results. It is observed that the shape of the input Tensor significantly affects the compression rate. Applied to data of channel turbulent flow, the Tensor Train format allows for surprisingly high compression rates whilst ensuring low relative errors.Keywords self-similarity; turbulent flows; Tensor Train format 1 IntroductionMultidimensional data sets, data of dimension 3 or higher, require massive storage capacity that strongly depends on the (Tensor) dimension, d, and on the number of entities per dimension, n. The datasize or storage requirement scales with O(n d ), n = max i {n i }. It is that curse of dimensionality that makes it difficult to handle higher-order Tensors or big data in an appropriate manner. Tensor product decomposition methods, [12], were originally developed to yield low-rank, i.e. data-sparse, representations or approximations of high-dimensional data in mathematical issues. It has been shown that those methods are as good as approximations by classical functions, e.g., like polynomials and wavelets, and that they allow very compact representations of large-data sets. Novel developments focus on hierarchical Tensor formats as e.g. the Tree-Tucker format, [10], and the Tensor Train format, [25], [11]. Nowadays, those hierarchical methods are successfully applied in e.g., physics or chemistry, where they are used in many body problems and quantum states.Here, we apply the Tensor Train decomposition to data of a 3D direct numerical simulation (DNS) of a turbulence channel flow. We aim at capturing self-similar structures that Th. von Larcher

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Towards a Framework for the Stochastic Modelling of Subgrid Scale Fluxes for Large Eddy Simulation

Cited by 4 publications

References 0 publications

A perspective on machine learning methods in turbulence modeling

A perspective on machine learning methods in turbulence modeling

A Perspective on Machine Learning Methods in Turbulence Modelling

On identification of self-similar characteristics using the Tensor Train decomposition method with application to channel turbulence flow

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