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Stabilization of the Spectral-Element Method in Turbulent Flow Simulations

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Spectral and High Order Methods for Partial Differential Equations

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 76))

Abstract

The effect of over-integration and filter-based stabilization in the spectral-element method is investigated. There is a need to stabilize the SEM for flow problems involving non-smooth solutions, e.g., turbulent flow simulations. In model problems such as the Burgers’ equation (similar to Kirby and Karniadakis, J. Comput. Phys. 191:249–264, 2003) and the scalar transport equation together with full Navier–Stokes simulations it is noticed that over-integration with the full 3/2-rule is not required for stability. The first additional over-integration nodes are the most efficient to remove aliasing errors. Alternatively, filter-based stabilization can in many cases alone help to stabilize the computation.

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Authors and Affiliations

  1. Linné Flow Centre, KTH Mechanics, Stockholm, Sweden

    J. Ohlsson, P. Schlatter & D. S. Henningson

  2. MCS, Argonne National Laboratory, Argonne, USA

    P. F. Fischer

Authors
  1. J. Ohlsson
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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 J. Ohlsson .

Editor information

Editors and Affiliations

  1. , Division of Applied Mathematics, Brown University, George Street 182, Providence, 02912, Rhode Island, USA

    Jan S. Hesthaven

  2. , Department of Mathematical Sciences, Norwegian University of Science and Tech, Trondheim, 7491, Norway

    Einar M. Rønquist

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Ohlsson, J., Schlatter, P., Fischer, P.F., Henningson, D.S. (2011). Stabilization of the Spectral-Element Method in Turbulent Flow Simulations. In: Hesthaven, J., Rønquist, E. (eds) Spectral and High Order Methods for Partial Differential Equations. Lecture Notes in Computational Science and Engineering, vol 76. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15337-2_43

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