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Dimension reduction in fluid dynamics equations

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Abstract

A method for transforming the Euler and Navier-Stokes equations and a complete system of fluid dynamics equations in three dimensions to a closed system on any moving surface is proposed. As a result, for an arbitrary geometric configuration, the dimension of the equations is reduced by one, which makes them convenient for numerical simulation. The general principles of the method are described, and verifying examples are presented.

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Authors and Affiliations

  1. Nuclear Safety Institute, Russian Academy of Sciences, ul. Bolshaya Tulskaya 52, Moscow, 115191, Russia

    V. B. Akkerman & M. L. Zaytsev

Authors
  1. V. B. Akkerman
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  2. M. L. Zaytsev
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Correspondence to V. B. Akkerman.

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Original Russian Text © V.B. Akkerman, M.L. Zaytsev, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 8, pp. 1518–1530.

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Akkerman, V.B., Zaytsev, M.L. Dimension reduction in fluid dynamics equations. Comput. Math. and Math. Phys. 51, 1418–1430 (2011). https://doi.org/10.1134/S0965542511080021

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  • DOI: https://doi.org/10.1134/S0965542511080021

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