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CABARET scheme in velocity-pressure formulation for two-dimensional incompressible fluids

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Abstract

The CABARET method was generalized to two-dimensional incompressible fluids in terms of velocity and pressure. The resulting algorithm was verified by computing the transport and interaction of various vortex structures: a stationary and a moving solitary vortex, Taylor-Green vortices, and vortices formed by the instability of double shear layers. Much attention was also given to the modeling of homogeneous isotropic turbulence and to the analysis of its spectral properties. It was shown that, regardless of the mesh size, the slope of the energy spectra up to the highest-frequency harmonics is equal −3, which agrees with Batchelor’s enstrophy cascade theory.

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Authors and Affiliations

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

    V. Yu. Glotov & V. M. Goloviznin

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  1. V. Yu. Glotov
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  2. V. M. Goloviznin
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Correspondence to V. Yu. Glotov.

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Original Russian Text © V.Yu. Glotov, V.M. Goloviznin, 2013, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2013, Vol. 53, No. 6, pp. 898–913.

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Glotov, V.Y., Goloviznin, V.M. CABARET scheme in velocity-pressure formulation for two-dimensional incompressible fluids. Comput. Math. and Math. Phys. 53, 721–735 (2013). https://doi.org/10.1134/S0965542513060080

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  • DOI: https://doi.org/10.1134/S0965542513060080

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