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

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Abstract

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. However, the results indicate that representation of highly irregular flows at low ranks cannot be expected.

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Acknowledgements

This research has been funded by Deutsche Forschungsgemeinschaft (DFG) through grant CRC 1114 ‘Scaling Cascades in Complex Systems’, Project B04 ‘Multiscale Tensor decomposition methods for partial differential equations’. The authors thank Prof. Illia Horenko (CRC 1114 Mercator Fellow) as well as Prof. Reinhold Schneider and Prof. Harry Yserentant for rich discussions and for steady support. Thomas von Larcher thanks Sebastian Wolf and Benjamin Huber (both at TU Berlin, Germany) very much for developing the Tensor library Xerus which has been used for data analysis, as well as for their round-the-clock support in the project. The data were generated and processed using resources of the North-German Supercomputing Alliance (HLRN), Germany, and of the Department of Mathematics and Computer Science, Freie Universität Berlin, Germany. The authors thank Alexander Kuhn and Christian Hege (both at Zuse Institute Berlin, Germany) for steady support in data processing and data visualization.

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  1. Waterloostraat 103A, 3062TJ, Rotterdam, The Netherlands

    Thomas von Larcher

  2. Institute of Mathematics, Freie Universität Berlin, Arnimallee 6, 14195, Berlin, Germany

    Rupert Klein

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Communicated by Oleg V. Vasilyev.

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Thomas von Larcher: formerly Freie Universität Berlin.

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von Larcher, T., Klein, R. On identification of self-similar characteristics using the Tensor Train decomposition method with application to channel turbulence flow. Theor. Comput. Fluid Dyn. 33, 141–159 (2019). https://doi.org/10.1007/s00162-019-00485-z

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