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An algebraic variational multiscale-multigrid method for large-eddy simulation: generalized-α time integration, Fourier analysis and application to turbulent flow past a square-section cylinder

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Abstract

This article studies three aspects of the recently proposed algebraic variational multiscale-multigrid method for large-eddy simulation of turbulent flow. First, the method is integrated into a second-order-accurate generalized-α time-stepping scheme. Second, a Fourier analysis of a simplified model problem is performed to assess the impact of scale separation on the overall performance of the method. The analysis reveals that scale separation implemented by projective operators provides modeling effects very close to an ideal small-scale subgrid viscosity, that is, it preserves low frequencies, in contrast to non-projective scale separations. Third, the algebraic variational multiscale-multigrid method is applied to turbulent flow past a square-section cylinder. The computational results obtained with the method reveal, on the one hand, the good accuracy achievable for this challenging test case already at a rather coarse discretization and, on the other hand, the superior computing efficiency, e.g., compared to a traditional dynamic Smagorinsky modeling approach.

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Authors and Affiliations

  1. Emmy Noether Research Group “Computational Multiscale Methods for Turbulent Combustion”, Technische Universität München, Boltzmannstr. 15, 85747, Garching, Germany

    Volker Gravemeier

  2. Institute for Computational Mechanics, Technische Universität München, Boltzmannstr. 15, 85747, Garching, Germany

    Volker Gravemeier, Michael W. Gee & Wolfgang A. Wall

  3. Division of Scientific Computing, Uppsala Universitet, Box 337, 751 05, Uppsala, Sweden

    Martin Kronbichler

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  1. Volker Gravemeier
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  2. Martin Kronbichler
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  4. Wolfgang A. Wall
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Correspondence to Volker Gravemeier.

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Gravemeier, V., Kronbichler, M., Gee, M.W. et al. An algebraic variational multiscale-multigrid method for large-eddy simulation: generalized-α time integration, Fourier analysis and application to turbulent flow past a square-section cylinder. Comput Mech 47, 217–233 (2011). https://doi.org/10.1007/s00466-010-0541-x

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