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Stochastic closure for local averages in the finite-difference discretization of the forced Burgers equation

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Abstract

We present a new approach for the construction of stochastic subgrid scale parameterizations. Starting from a high-resolution finite-difference discretization of some model equations, the new approach is based on splitting the model variables into fast, small-scale and slow, large-scale modes by averaging the model discretization over neighboring grid cells. After that, the fast modes are eliminated by applying a stochastic mode reduction procedure. This procedure is a generalization of the mode reduction strategy proposed by Majda, Timofeyev & Vanden-Eijnden, in that it allows for oscillations in the closure assumption. The new parameterization is applied to the forced Burgers equation and is compared with a Smagorinsky-type subgrid scale closure.

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Authors and Affiliations

  1. Institut für Atmosphäre und Umwelt, Goethe-Universität Frankfurt, Altenhöferallee 1, 60438, Frankfurt am Main, Germany

    S. I. Dolaptchiev & U. Achatz

  2. Department of Mathematics, University of Houston, Houston, TX, USA

    I. Timofeyev

Authors
  1. S. I. Dolaptchiev
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  2. U. Achatz
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  3. I. Timofeyev
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Correspondence to S. I. Dolaptchiev.

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Communicated by R. Klein.

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Dolaptchiev, S.I., Achatz, U. & Timofeyev, I. Stochastic closure for local averages in the finite-difference discretization of the forced Burgers equation. Theor. Comput. Fluid Dyn. 27, 297–317 (2013). https://doi.org/10.1007/s00162-012-0270-1

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