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Vortex Scattering of Monatomic Gas Along Plane Curves

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Abstract

An invariant submodel of gas dynamics equations constructed on a three-dimensional subalgebra with a projective operator for the case of monatomic gas is under consideration. The submodel is reduced to an Abel equation, with integral curves constructed for it. For a separatrix of a saddle, an approximate solution is studied. Such solutions describe the vortex scattering of gas along plane curves placed on the surface of revolution.

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References

  1. L. V. Ovsyannikov, “SUBMODEL Program. Gas Dynamics,” Prikl. Mat. Mekh. 58 (4), 30–55 (1994).

    MathSciNet  Google Scholar 

  2. A. A. Cherevko, “An Optimal System of Subalgebras for the Lie Algebra of Operators Allowed by the System of Gas Dynamics Equations of with the State Equation p = f(S)ρ5/3,” Preprint No. 4-96 (Lavrent’ev Inst. of Hydrodynamics, Sib. Branch, Russian Acad. of Sci., Novosibirsk, 1996).

    Google Scholar 

  3. S. V. Golovin, Submodels of the Polytropic Gas Dynamics: Thesis of a Candidate of Physical and Mathematical Sciences (Novosibirsk, 2000) [in Russian].

    Google Scholar 

  4. R. F. Shayakhmetova, “Embedded Invariant Submodels of the Motion of Monatomic Gas,” Sib. Elektron. Mat. Izv. 11, 605–625 (2014).

    MathSciNet  MATH  Google Scholar 

  5. A. A. Nikolskii, “Invariant Transformation of Motion Equations of Ideal Monatomic Gas and New Classes of Their Exact Solutions,” Prikl. Mat. Mekh. 27 (3), 496–508 (1963).

    Google Scholar 

  6. L. I. Sedov, Similarity and Dimensional Methods in Mechanics (Gostekhteoretizdat, Moscow, 1954; Academic Press, 1959).

    Google Scholar 

  7. S. V. Khabirov, “Nonstationary Invariant Solution of the Gas Dynamics Equations Describing the Spreading of Gas to Vacuum,” Prikl. Mat. Mekh. 52 (6), 967–975 (1988).

    MathSciNet  MATH  Google Scholar 

  8. A. S. Pavlenko, “Symmetry and Solutions of Equations of Two-Dimensional Movements of Polytropic Gas,” Sib. Elektron. Mat. Izv. 2, 291–307 (2005).

    MATH  Google Scholar 

  9. A. S. Pavlenko, “Projective Submodel of the Ovsyannikov Vortex,” Prikl. Mekh. Tekh. Fiz. 46 (4), 3–16 (2005) [J. Appl. Mech. Tech. Phys. 46 (4), 459–470 (2005)].

    MathSciNet  MATH  Google Scholar 

  10. A. A. Chesnokov “Symmetries and Exact Solutions of the Shallow Water Equations for a Two-Dimensional Shear Flow,” Prikl. Mekh. Tekh. Fiz. 49 (5), 41–54 (2008) [J. Appl. Mech. Tech. Phys. 49 (5), 737–748 (2008)].

    Google Scholar 

  11. A. M. Barlukova and A. P. Chupakhin, “Partially Invariant Solutions in Gas Dynamics and Implicit Equations,” Prikl. Mekh. Tekh. Fiz. 53 (6), 11–24 (2012) [J. Appl. Mech. Tech. Phys. 53 (6), 812–824 (2012)].

    MathSciNet  MATH  Google Scholar 

  12. S. V. Golovin, “An Invariant Solution of Gas Dynamics Equations,” Prikl. Mekh. Tekh. Fiz. 38 (1), 3–10 (1997) [J. Appl. Mech. Tech. Phys. 38 (1), 1–7 (1997)].

    Google Scholar 

  13. S. V. Golovin, “Exact Solutions for Evolutionary Submodels of Gas Dynamics,” Prikl. Mekh. Tekh. Fiz. 43 (4), 3–14 (2002) [J. Appl. Mech. Tech. Phys. 43 (4), 493–502 (2002)].

    MATH  Google Scholar 

  14. R. F. Shayakhmetova, “Vortex Scattering of Monatomic Gas,” in Proc. of the Institute of Mechanics of Ufa Scientific Center of the Russian Academy of Sciences, Vol. 10 (2014), pp. 110–113.

    MATH  Google Scholar 

  15. V. F. Zaitsev and A. D. Polyanin, Handbook on Ordinary Differential Equations (Fizmatlit, Moscow, 2001) [in Russian].

    MATH  Google Scholar 

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Correspondence to R. F. Shayakhmetova.

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Original Russian Text © R.F. Shayakhmetova.

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 2, pp. 63–73, March–April, 2018.

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Shayakhmetova, R.F. Vortex Scattering of Monatomic Gas Along Plane Curves. J Appl Mech Tech Phy 59, 241–250 (2018). https://doi.org/10.1134/S0021894418020074

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  • DOI: https://doi.org/10.1134/S0021894418020074

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