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| Titel |
A non-statistical regularization approach and a tensor product decomposition method applied to complex flow data |
| VerfasserIn |
Thomas von Larcher, Therese Blome, Rupert Klein, Reinhold Schneider, Sebastian Wolf, Benjamin Huber |
| Konferenz |
EGU General Assembly 2016
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 18 (2016) |
| Datensatznummer |
250129540
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| Publikation (Nr.) |
 EGU/EGU2016-9668.pdf |
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| Zusammenfassung |
| Handling high-dimensional data sets like they occur e.g. in turbulent flows or in multiscale
behaviour of certain types in Geosciences are one of the big challenges in numerical analysis
and scientific computing. A suitable solution is to represent those large data sets in an
appropriate compact form. In this context, tensor product decomposition methods currently
emerge as an important tool. One reason is that these methods often enable one to attack
high-dimensional problems successfully, another that they allow for very compact
representations of large data sets.
We follow the novel Tensor-Train (TT) decomposition method to support the
development of improved understanding of the multiscale behavior and the development of
compact storage schemes for solutions of such problems. One long-term goal of the project is
the construction of a self-consistent closure for Large Eddy Simulations (LES) of turbulent
flows that explicitly exploits the tensor product approach’s capability of capturing self-similar
structures.
Secondly, we focus on a mixed deterministic-stochastic subgrid scale modelling strategy
currently under development for application in Finite Volume Large Eddy Simulation (LES)
codes. Advanced methods of time series analysis for the databased construction of
stochastic models with inherently non-stationary statistical properties and concepts of
information theory based on a modified Akaike information criterion and on the
Bayesian information criterion for the model discrimination are used to construct
surrogate models for the non-resolved flux fluctuations. Vector-valued auto-regressive
models with external influences form the basis for the modelling approach [1], [2],
[4].
Here, we present the reconstruction capabilities of the two modeling approaches tested
against 3D turbulent channel flow data computed by direct numerical simulation (DNS) for
an incompressible, isothermal fluid at Reynolds number Reτ = 590 (computed by
[3]).
References
[1] I. Horenko. On identification of nonstationary factor models and its application to
atmospherical data analysis. J. Atm. Sci., 67:1559-1574, 2010.
[2] P. Metzner, L. Putzig and I. Horenko. Analysis of persistent non-stationary time series
and applications. CAMCoS, 7:175-229, 2012.
[3] M. Uhlmann. Generation of a temporally well-resolved sequence
of snapshots of the flow-field in turbulent plane channel flow. URL:
http://www-turbul.ifh.unikarlsruhe.de/uhlmann/reports/produce.pdf, 2000.
[4] Th. von Larcher, A. Beck, R. Klein, I. Horenko, P. Metzner, M. Waidmann, D.
Igdalov, G. Gassner and C.-D. Munz. Towards a Framework for the Stochastic Modelling of
Subgrid Scale Fluxes for Large Eddy Simulation. Meteorol. Z., 24:313-342, 2015. |
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