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Differentially invariant solutions of equations of plane steady flows of a viscous heat-conducting perfect gas with a polytropic equation of state

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Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

A system of Navier-Stokes equations for two-dimensional steady flows of a viscous heatconducting perfect gas with a polytropic equation of state is considered. Differentially invariant solutions of this system are studied. Bases of differential invariants and operators of invariant differentiation are constructed for all subgroups of the admitted group. Examples of new differentially invariant solutions are obtained.

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References

  1. V. V. Bublik, “Regular, Partially Invariant Solutions of Rank 1 and Defect 1 of Equations of Plane Motion of a Viscous Heat-Conducting Gas,” Prikl. Mekh. Tekh. Fiz. 47(6), 23–33 (2006) [J. Appl. Mech. Tech. Phys. 47 (6), 790–799 (2006)].

    MathSciNet  MATH  Google Scholar 

  2. S. V. Meleshko, “Group Classification of Two-Dimensional Stable Viscous Gas Equations,” Int. J. Nonlinear Mech. 34(3), 449–456 (1998).

    Article  MathSciNet  ADS  Google Scholar 

  3. S. V. Meleshko, “Group Classification of Two-Dimensional Steady Viscous Gas Dynamics Equations with Arbitrary State Equations,” J. Phys. A: Math. Gen., No. 35, 3515–3533 (2002).

  4. V. V. Bublik, “Invariant Solutions of Rank 1 of the Equations of Plane Motion of a Viscous Heat-Conducting Perfect Gas,” Prikl. Mekh. Tekh. Fiz. 38(3), 26–31 (1997) [J. Appl. Mech. Tech. Phys. 38 (3), 351–356 (1997)].

    MathSciNet  MATH  Google Scholar 

  5. V. K. Andreev, V. V. Bublik, and V. O. Bytev, Symmetries of Nonclassical Models of Hydrodynamics (Nauka, Novosibirsk, 2003) [in Russian].

    Google Scholar 

  6. V. V. Bublik, “Simple Solutions of Equations of Two-DimensionalMotions of a Viscous Heat-Conducting Perfect Gas,” in Dynamics of Continuous Media, No. 116 (Inst. Hydrodynamics, Sib. Branch, Russian Acad. of Sci., Novosibirsk, 2000), pp. 123–127.

    Google Scholar 

  7. I. A. Kaliev, “Some Exact Solutions of a System of Equations of a Viscous Gas,” in Dynamics of Continuous Media, No. 114 (Inst. Hydrodynamics, Sib. Branch, Russian Acad. of Sci., Novosibirsk, 1999), pp. 40–42.

    Google Scholar 

  8. V. V. Bublik, “Application of Computer Algebra Systems for Constructing Partially Invariant and Differentially Invariant Solutions,” Vychisl. Tekhnol. 12(5), 32–40 (2007).

    MATH  Google Scholar 

  9. L. V. Ovsyannikov, Group Analysis of Differential Equations (Nauka, Moscow, 1978; Academic Press, New York (1982).

    MATH  Google Scholar 

  10. S. V. Khabirov, “Classification of Differentially Invariant Submodels,” Sib. Mat. Zh. 45(3), 682–701 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  11. L. V. Ovsyannikov, “Regular and Irregular Partially Invariant Solutions,” Dokl. Ross. Akad. Nauk 343(2), 156–159 (1995).

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    V. V. Bublik

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  1. V. V. Bublik
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Correspondence to V. V. Bublik.

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Original Russian Text © V.V. Bublik.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 53, No. 2, pp. 14–20, March–April, 2012.

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Bublik, V.V. Differentially invariant solutions of equations of plane steady flows of a viscous heat-conducting perfect gas with a polytropic equation of state. J Appl Mech Tech Phy 53, 156–161 (2012). https://doi.org/10.1134/S0021894412020022

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  • DOI: https://doi.org/10.1134/S0021894412020022

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