IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i1p123-d716014.html
   My bibliography  Save this article

New Exact Solutions with a Linear Velocity Field for the Gas Dynamics Equations for Two Types of State Equations

Author

Listed:
  • Renata Nikonorova

    (Mavlyutov Institute of Mechanics, Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, 450054 Ufa, Russia)

  • Dilara Siraeva

    (Mavlyutov Institute of Mechanics, Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, 450054 Ufa, Russia)

  • Yulia Yulmukhametova

    (Mavlyutov Institute of Mechanics, Subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, 450054 Ufa, Russia)

Abstract

In this paper, exact solutions with a linear velocity field are sought for the gas dynamics equations in the case of the special state equation and the state equation of a monatomic gas. These state equations extend the transformation group admitted by the system to 12 and 14 parameters, respectively. Invariant submodels of rank one are constructed from two three-dimensional subalgebras of the corresponding Lie algebras, and exact solutions with a linear velocity field with inhomogeneous deformation are obtained. On the one hand of the special state equation, the submodel describes an isochoric vortex motion of particles, isobaric along each world line and restricted by a moving plane. The motions of particles occur along parabolas and along rays in parallel planes. The spherical volume of particles turns into an ellipsoid at finite moments of time, and as time tends to infinity, the particles end up on an infinite strip of finite width. On the other hand of the state equation of a monatomic gas, the submodel describes vortex compaction to the origin and the subsequent expansion of gas particles in half-spaces. The motion of any allocated volume of gas retains a spherical shape. It is shown that for any positive moment of time, it is possible to choose the radius of a spherical volume such that the characteristic conoid beginning from its center never reaches particles outside this volume. As a result of the generalization of the solutions with a linear velocity field, exact solutions of a wider class are obtained without conditions of invariance of density and pressure with respect to the selected three-dimensional subalgebras.

Suggested Citation

  • Renata Nikonorova & Dilara Siraeva & Yulia Yulmukhametova, 2022. "New Exact Solutions with a Linear Velocity Field for the Gas Dynamics Equations for Two Types of State Equations," Mathematics, MDPI, vol. 10(1), pages 1-20, January.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:1:p:123-:d:716014
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/1/123/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/1/123/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:1:p:123-:d:716014. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.