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Time averaging as an approximate technique for constructing quasi-gasdynamic and quasi-hydrodynamic equations

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Abstract

Quasi-gasdynamic and quasi-hydrodynamic equations for compressible gas flows and viscous incompressible fluid flows are constructed by averaging the corresponding Navier-Stokes equations over time with the use of certain approximations.

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References

  1. B. N. Chetverushkin, Kinetically Consistent Schemes in Gas Dynamics (Mosk. Gos. Univ., Moscow, 1999) [in Russian].

    Google Scholar 

  2. B. N. Chetverushkin, Kinetic Schemes and Quasi-Gasdynamic System of Equations (Maks Press, Moscow, 2004) [in Russian].

    Google Scholar 

  3. Yu. V. Sheretov, Mathematical Modeling of Fluid Flows Based on Quasi-Hydrodynamic and Quasi-Gasdynamic Equations (Tversk. Gos. Univ., Tver, 2000) [in Russian].

    Google Scholar 

  4. T. G. Elizarova, Quasi-Gasdynamic Equations and Methods for Computing Viscous Flows (Nauchnyi Mir, Moscow, 2007) [in Russian].

    Google Scholar 

  5. T. G. Elizarova, Quasi-Gas Dynamic Equations (Springer-Verlag, Berlin, 2009).

    Book  MATH  Google Scholar 

  6. Yu. V. Sheretov, Dynamics of Continuum Media under Spatiotemporal Averaging (RKhD, Moscow, 2009) [in Russian].

    Google Scholar 

  7. Yu. V. Sheretov, “On General Exact Solutions of the Navier-Stokes, Euler, and Quasi-Gas Dynamic Equations,” Vestn. Tversk. Gos. Univ., Ser. Prikl. Mat., No. 14, 41–58 (2010).

  8. Yu. V. Sheretov, “Quasi-Gas Dynamic Equations and Analytical Functions,” in Application of Functional Analysis in Approximation Theory (Tversk. Gos. Univ., Tver, 2010), pp. 61–67 [in Russian].

    Google Scholar 

  9. L. G. Loitsyanskii, Mechanics of Liquids and Gases (Begell House, New York, 1996; Drofa, Moscow, 2003).

    Google Scholar 

  10. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Nauka, Moscow, 1986; Pergamon Press, Oxford, 1987).

    Google Scholar 

  11. A. A. Zlotnik, “On the Quasi-Gas System of Equations with a Generalized Equation of State and Heat Sources,” Mat. Model. 22 (7), 5–64 (2010).

    Google Scholar 

  12. T. G. Elizarova and O. V. Bulatov, “Regularized Shallow Water Equations and a New Method of Simulation of the Open Channel Flows,” Compt Fluids, No. 46, 206–211 (2011).

  13. T. G. Elizarova and S. D. Ustyugov, Preprint No. 30, IPM RAN (Keldysh Inst. of Applied Mathematics, Russian Academy of Sciences, Moscow, 2010).

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Authors and Affiliations

  1. Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

    T. G. Elizarova

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  1. T. G. Elizarova
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Correspondence to T. G. Elizarova.

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Original Russian Text © T.G. Elizarova, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 11, pp. 2096–2105.

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Elizarova, T.G. Time averaging as an approximate technique for constructing quasi-gasdynamic and quasi-hydrodynamic equations. Comput. Math. and Math. Phys. 51, 1973–1982 (2011). https://doi.org/10.1134/S0965542511110078

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  • DOI: https://doi.org/10.1134/S0965542511110078

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