Solution of the Ovsyannikov Problem of Two-Dimensional Isothermal Motion of a Polytropic Gas

Article

Abstract

We study an overdetermined system of partial differential equations which describes the two-dimensional isothermal motion of a polytropic gas. The system is reduced to a passive form and is completely integrated. The resulting solutions are treated as ideal incompressible fluid flows bounded by a free surface or a moving solid wall.

Keywords

isothermal gas flows thermal motion of gas free-boundary ideal flow overdetermined systems exact solutions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. V. Ovsyannikov, “Simple Solutions of the Equations of Dynamics for a Polytropic Gas,” Prikl. Mat. Tekh. Fiz. 40 (2), 5–12 (1999) [J. Appl. Mech. Mech. Tech. Phys. 40 (2), 191–197 (1999)].MathSciNetMATHGoogle Scholar
  2. 2.
    M. V. Neshchadim and A. P. Chupakhin, “Some Solutions of the Equations of Motion of a Continuous Medium with Special Thermodynamics,” Sib. Elektron. Mat. Izv. 8, 317–332 (2011).MATHGoogle Scholar
  3. 3.
    L. V. Ovsyannikov, “Isobaric Gas Motion,” Differ. Uravn. 30 (10), 1792–1799 (1994).MathSciNetGoogle Scholar
  4. 4.
    N. A. Inogamov, “Cylindrical Analog of Trochoidal Gerstner Waves,” Izv. Akad. Nauk, Mekh. Zhidk. Gaza 20 (5), 145–150 (1985).MathSciNetMATHGoogle Scholar
  5. 5.
    Yu. V. Shan’ko, “On an Overdetermined System of Equations of Motion of a Continuous Medium,” in Reshetnev Readings, Proc. of the 17th Int. Sci. Conf., Krasnoyarsk, November 12–14, 2013 (Sib. Gos. Aerokosm. Univ., Krasnoyarsk, 2013), Part 2, pp. 122–123.Google Scholar
  6. 6.
    S. V. Khabirov, “General Solution of a Planar Hydrodynamic Model of Motion with a One-Parameter Thermodynamic System and Variable Entropy,” in New Mathematical Models of Continuum Mechanics: Construction and Investigation, Abstracts of the All Russian Conf. Novosibirsk, April 18–22, 2014 (Lavrentyev Institute of Hydrodynamics, Sib. Branch, Russian Acad. of Sci., Novosibirsk, 2014), pp. 140–141.Google Scholar
  7. 7.
    S. V. Khabirov, “Plane Isothermal Motion of an Ideal Gas without Expansion,” Prikl. Mat. Mekh. 78 (3), 411–424 (2014).MathSciNetGoogle Scholar
  8. 8.
    A. C. Hearn and R. Schopf, REDUCE User’s Manual; http://reduce-algebra.sourceforge.net/manual/manual.html.Google Scholar
  9. 9.
    S. P. Finikov, Method of Cartan External Forms in Differential Geometry (Gostekhteoretizdat, Moscow, Leningrad, 1948) [in Russian].MATHGoogle Scholar
  10. 10.
    P. K. Rashevskii, Course in Differential Geometry (Gostekhteoretizdat, Moscow–Leningrad, 1950) [in Russian].Google Scholar
  11. 11.
    A. A. Abrashkin and E. I. Yakubovich, Vortex Dynamics in Lagrangian Description (Fizmatlit, Moscow, 2006) [in Russian].Google Scholar
  12. 12.
    V. I. Nalimov and V. V. Pukhnachov, Unsteady Motion of an Ideal Fluid with a Free Boundary (Novosib. Gos. Univ., Novosibirsk, 1975) [in Russian].Google Scholar
  13. 13.
    Yu. V. Shan’ko, “Analysis of Overdetermined System that Describes the Special Class of Two-Dimensional Motion of an Ideal Fluid,” http://arxiv.org/abs/1608.08186.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Institute of Computational Modeling, Siberian BranchRussian Academy of SciencesKrasnoyarskRussia

Personalised recommendations