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Parameter-free method for computing the turbulent flow in a plane channel in a wide range of Reynolds numbers

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Abstract

Near-wall turbulence in a plane channel at high Reynolds numbers is studied by applying direct numerical simulation. A new numerical algorithm is proposed in which convective fluxes are explicitly approximated using the CABARET scheme and two grid elliptic equations are solved in order to satisfy the incompressibility condition. The equations are of high dimension and are solved by employing a fast direct method that can be efficiently parallelized. In contrast to most methods, including spectral ones, the CABARET scheme does not involve any tuning parameters. It has a compact stencil, which simplifies setting boundary conditions and improves the efficiency of parallelization in computations on multiprocessor computer systems. Numerical results are obtained in a wide range of Reynolds numbers and are compared with experimental data and numerical results of other authors. The error in the computed drag coefficient for turbulent flow is examined as a function of grid characteristics.

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Authors and Affiliations

  1. Nuclear Safety Institute, Russian Academy of Sciences, Bol’shaya Tul’skaya ul. 52, Moscow, 115191, Russia

    D. G. Asfandiyarov & S. A. Finogenov

  2. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia

    V. M. Goloviznin

Authors
  1. D. G. Asfandiyarov
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  2. V. M. Goloviznin
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  3. S. A. Finogenov
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Correspondence to D. G. Asfandiyarov.

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Original Russian Text © D.G. Asfandiyarov, V.M. Goloviznin, S.A. Finogenov, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 9, pp. 1545–1558.

In blessed memory of A.P. Favorskii

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Asfandiyarov, D.G., Goloviznin, V.M. & Finogenov, S.A. Parameter-free method for computing the turbulent flow in a plane channel in a wide range of Reynolds numbers. Comput. Math. and Math. Phys. 55, 1515–1526 (2015). https://doi.org/10.1134/S096554251509002X

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  • DOI: https://doi.org/10.1134/S096554251509002X

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