Fluid Dynamics

, Volume 53, Issue 1, pp 143–151 | Cite as

Unsteady Rarefied Gas Flow with Shock Wave in a Channel

  • V. A. Titarev
  • E. M. Shakhov


The two-dimensional time-dependent problem of rarefied gas flow in a plane channel, formed by parallel plates of finite length and closed at one end, is solved on the basis of the kinetic S-model. The flow develops as a result of rupture of a diaphragm which separates the gas at rest in the channel and the gas at rest in a reservoir of infinite volume. The effect of gas deceleration at the channel walls under the conditions of diffuse molecular reflection from the channel walls and end face is studied. Decay of a shock wave and disappearance of a homogeneous flow zone behind the shock wave is traced for three variants of conditions at the channel inlet: (1) gas enters the channel from a reservoir of infinite length and width (as the basic variant), the simultaneous motion in the reservoir and channel being studied; (2) the high-pressure reservoir represents a usual channel section; and (3) the motion of the gas in the reservoir is not considered at all, instead of this, the boundary conditions of the evaporation-condensation type under the conditions of gas at rest in the reservoir are imposed in the inlet cross-section.

Key words

rarefied gas breakdown of a discontinuity kinetic S-model shock wave TVD-scheme 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F. Sharipov and V. Seleznev, “Data on Internal Rarefied Gas Flows,” J. Phys. Chem. Ref. Data 27 (3), 657–706 (1998).ADSCrossRefGoogle Scholar
  2. 2.
    F. Sharipov and V. Seleznev, Rarefied Gas Flows in Channels and Microchannels (Ural Branch of RAS, Ekaterinburg, 2008).Google Scholar
  3. 3.
    N. Mioshi, S. Nagata, I. Kinefuchi, K. Shimizu, S. Takagi, and Y. Matsumoto, “Development of Ultra Small Shock Tube for High Energy Molecular Beam Source,” in: 26th Internat. Symp. Rarefied Gas Dynamics. AIP Conf. Proc. (Melville, New York, 2009), Vol. 1084, pp. 557–562.ADSGoogle Scholar
  4. 4.
    I. N. Larina, V. A. Rykov, and E. M. Shakhov, “Development of Rarefied Gas Flow between Parallel Plates Due to an Initial Jump in Pressure,” Dokl. Ross. Akad. Nauk 343 (4), 482–485 (1995).zbMATHGoogle Scholar
  5. 5.
    I. N. Larina, V. A. Rykov, and E. M. Shakhov, “Unsteady Rarefied-Gas Flow between Parallel Plates,” Fluid Dynamics 32 (2), 289–295 (1997).zbMATHGoogle Scholar
  6. 6.
    F. Sharipov, “Transient Flow of Rarefied Gas through a Short Tube,” Vacuum 90, 25–30 (2013).ADSCrossRefGoogle Scholar
  7. 7.
    F. Sharipov and I. A. Graur, “General Approach to Transient Flows of Rarefied Gas through Long Capillaries,” Vacuum 100, 22–25 (2013).ADSCrossRefGoogle Scholar
  8. 8.
    D. E. Zeitoun, I. A. Graur, Y. Burtschell, M. S. Ivanov, A. N. Kudryavtsev, and Ye. A. Bondar, “Continuum and Kinetic Simulation of Shock Wave Propagation in Long Microchannel,” in: Rarefied Gas Dynamics. 26th Intern. Symposium on RGD. Ed. T. Abe, AIP Conference Proceedings (Melville, New York, 2009), Vol. 1084, pp. 964–969.Google Scholar
  9. 9.
    Yu. Yu. Kloss, F. G. Cheremisin, and P.V. Shuvalov, “Solution of the Boltzmann Equation forUnsteady Flows with ShockWaves in Narrow Channels,” Zh. Vychisl.Matem.Matemat. Fiz. 50 (6), 1148–1158 (2010).zbMATHGoogle Scholar
  10. 10.
    N. A. Konopel’ko, V. A. Titarev, and E. M. Shakhov, “Rarefied Gas Deceleration in a Plane Channel in the Case of Expansion into a Vacuum,” Fluid Dynamics 50 (2), 294–305 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    N. A. Konopel’ko, V. A. Titarev, and E. M. Shakhov, “Unsteady RarefiedGas Flow in aMicrochannel Initiated by Breakdown of a Pressure Discontinuity,” Zh. Vychisl.Matem.Matemat. Fiz. 56 (3), 476–489 (2016).Google Scholar
  12. 12.
    E. M. Shakhov, “Generalization of the Krook Kinetic Relaxation Equation,” Fluid Dynamics 3 (5), 95–96 (1968).ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    V. A. Titarev, “Nesvetay-3D ProgrammSoftware for Simulating Plane Flows of aMonatomic Rarefied Gas,” Certificate of State Registration of Computer Programs No. 2017616295 (2017).Google Scholar
  14. 14.
    V. A. Titarev, “Implicit Numerical Method of Calculating Three-Dimensional Rarefied Gas Flows with the Use of Unstructured Grids,” Zh. Vychisl.Matem.Matemat. Fiz. 50 (10), 1811–1826 (2010).MathSciNetzbMATHGoogle Scholar
  15. 15.
    V. A. Titarev, “Efficient Deterministic Modelling of Three-Dimensional Rarefied Gas Flows,” Commun. Comput. Phys. 12 (1), 161–192 (2012).MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    V. A. Titarev, “Nesvetai-3D Programm Software for Simulating Three-Dimensional Flows of a Monatomic Rarefied Gas,” Nauka i Obrazovanie. Bauman Moscow State Technical University. Electronic Zh. 6, 124–154 (2014).Google Scholar
  17. 17.
    V. A. Titarev, S. V. Utyuzhnikov, and A. V. Chikitkin, “OpenMP + MPI Parallel Implementation of the Numerical Method for Solving the Kinetic Equation,” Zh. Vychisl. Matem. Matemat. Fiz. 56 (11), 1949–1959 (2016).MathSciNetzbMATHGoogle Scholar
  18. 18.
    A. Semin, E. Druzhinin, V. Mironov, A. Shmelev, and A. Moskovsky, “The Performance Characterization of the RSC PetaStream Module,” in: Lecture Notes in Computer Science. 2014 (29th International Conference, ISC 2014, Leipzig, Germany, 2014), Vol. 8488, pp. 420–429.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Federal Research Center “Computer Science and Control” of the Russian Academy of SciencesMoscowRussia
  2. 2.Bauman Moscow State Technical UniversityMoscowRussia

Personalised recommendations