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Stability Tools for the Spectral-Element Code Nek5000: Application to Jet-in-Crossflow

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Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 95))

Abstract

We demonstrate the use of advanced linear stability tools developed for the spectral-element code Nek5000 to investigate the dynamics of nonlinear flows in moderately complex geometries. The aim of stability calculations is to identify the driving mechanism as well as the region most sensitive to the instability: the wavemaker. We concentrate on global linear stability analysis, which considers the linearised Navier–Stokes equations and searches for growing small disturbances, i.e. so-called linear global modes. In the structural sensitivity analysis these modes are associated to the eigenmodes of the direct and adjoint linearised Navier–Stokes operators, and the wavemaker is defined as the overlap of the strongest direct and adjoint eigenmodes. The large eigenvalue problems are solved using matrix-free methods adopting the time-stepping Arnoldi approach. We present here our implementation in Nek5000 with the ARPACK library on a number of test cases.

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Acknowledgements

We would like to thank O. Tammisola and I. Lashgari for help in developing and testing our implementation. Computer time was provided by Swedish National Infrastructure for Computing (SNIC). The third author was supported by the U.S. Department of Energy under Contract DE-AC02-06CH11357.

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Authors and Affiliations

  1. Linné FLOW Centre and Swedish e-Science Research Centre (SeRC), KTH Mechanics, Royal Institute of Technology, SE-100 44, Stockholm, Sweden

    A. Peplinski, P. Schlatter & D. S. Henningson

  2. MCS, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL, 60439, USA

    P. F. Fischer

Authors
  1. A. Peplinski
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  2. P. Schlatter
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  3. P. F. Fischer
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  4. D. S. Henningson
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Corresponding author

Correspondence to A. Peplinski .

Editor information

Editors and Affiliations

  1. Institut Polytechnique de Bordeaux, Université de Bordeaux, Pessac, France

    Mejdi Azaïez

  2. Ecole Nationale d'Ingénieurs de Tunis, Université de Tunis El Manar, Tunis, Tunisia

    Henda El Fekih

  3. EPFL-SB-MATHICSE-MCSS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Jan S. Hesthaven

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Peplinski, A., Schlatter, P., Fischer, P.F., Henningson, D.S. (2014). Stability Tools for the Spectral-Element Code Nek5000: Application to Jet-in-Crossflow. In: Azaïez, M., El Fekih, H., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012. Lecture Notes in Computational Science and Engineering, vol 95. Springer, Cham. https://doi.org/10.1007/978-3-319-01601-6_28

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