Skip to main content
SpringerLink
Log in

Programming and modelling environment for studies of gas flows in micro- and nanostructures based on solving the Boltzmann equation

  • Published:
Atomic Energy Aims and scope

A set of programs has been developed for modelling gas flows in micro-and nanostructures. The programs are based on a method for solving the kinetic equation by a finite-difference technique on a fixed space-velocity grid. A projection method is used for calculating the Boltzmann collision integral which ensures that the conservation of mass, momentum, and energy is rigorously satisfied and that the collision integral goes to zero under thermodynamic equilibrium conditions. An explicit flux conservative scheme is used for approximating the differential part. The solution of the resulting system of difference equations is found by splitting into stages of collisional relaxation and free molecular flow. The computational algorithm is realized on a multiprocessor system using MPI technology. A graphical shell has been developed for visualizing the results during the computations and for convenient variation of the physical parameters of the flow under study. Some calculations of flows through a periodic system of square holes and a periodic system of slots whose transverse dimension is on the order of the mean free path of the gas molecules, as well as some model calculations of a micropump design, are given as examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. N. Kogan, Rarefied Gas Dynamics [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  2. G. A. Bird, Molecular Gas Dynamics [Russian translation], Mir, Moscow (1981).

    Google Scholar 

  3. F. G. Cheremisin, “A conservative method for calculating the Boltzmann collision integral,” Doklady RAN, 357, No. 1, 1–4 (1997).

    Google Scholar 

  4. F. G. Cheremisin, “Solving the Boltzmann kinetic equation for high velocity flows,” Zh. Vychisl. Matem. Matem. Fiz., 46, No. 2, 329–343 (2006).

    MATH  MathSciNet  Google Scholar 

  5. S. P. Popov and F. G. Cheremisin, “A conservative method for solving the Boltzmann equation for centrally symmetric potentials,” Zh. Vychisl. Matem. Matem. Fiz., 39, No. 1, 163–176 (1999).

    MathSciNet  Google Scholar 

  6. V. V. Aristov and F. G. Cheremisin, “Splitting a nonuniform kinetic operator in the Boltzmann equation,” Dokl. AN SSSR, 231, No. 1, 49–52 (1976).

    ADS  Google Scholar 

  7. N. M. Korobov, Trigonometric Sums and Their Applications [in Russian], Nauka, Moscow (1989).

    MATH  Google Scholar 

  8. Yu. Yu. Kloss, N. I. Khokhlov, F. G. Cheremisin, and B. A. Shurygin, “Development of numerical schemes for solving the kinetic equation in cluster environments based on the MPI technology,” Inform. Protsessy, 7, No. 4, 425–431 (2007).

    Article  Google Scholar 

  9. G. Pham Van Diep, P. Keeley, E. Muntz, and D. Weaver, “A micromechanical Knudsen compressor, ” in: Int. Conf. on Rarefied Gas Dynamics, Oxford Univ. Press (1995), pp. 715–721.

  10. S. E. Vargo and E. P. Muntz, “An evaluation of a multiple stage micromechanical Knudsen compressor and vacuum pump,” in: Int. Conf. on Rarefied Gas Dynamics, Peking Univ. Press (1997), pp. 995–1000.

  11. S. Vargo and E. Muntz, “Initial results from the first MEMS fabricated thermal transpiration-driven vacuum pump,” in: Int. Conf. on Rarefied Gas Dynamics, Sydney (2000), pp. 467–473.

  12. Y.-L. Han, A. Alexeenko, M. Young, and E. Muntz, “Experimental and computational studies of temperature gradient driven molecular transport in gas flows through nano/micro-scale channels,” in: 2nd Int. Conf. on Transport Phenomena in Micro and Nanodevices, Barga, Italy (2006), pp. 581–601.

  13. E. Muntz, A. A. Alexeenko, S. F. Gimelshein, et al., “Low speed nano/micro/meso-scale rarefied flows driven by temperature and pressure gradients,” in: Int. Conf. on Rarefied Gas Dynamics, Novosibirsk (2007), pp. 781–790.

  14. H. Sugimoto and Y. Sone, “Vacuum pump without a moving part driven by thermal edge flow,” in: Int. Conf. on Rarefied Gas Dynamics, New York (2005), pp. 762–771.

  15. H. Sugimoto, S. Takata, and S. Kosuge, “Gas separation effect of the pump driven by the thermal edge flow,” in: Int. Conf. on Rarefied Gas Dynamics, Novosibirsk (2007), pp. 567–571.

  16. U. Kursun and J. Karpat, “Modeling of backward facing step gas flow in transition regime,” in: 2nd Int. Conf. on Transport Phenomena in Micro and Nanodevices, Barga, Italy (2006), pp. 662–669.

Download references

Author information

Authors and Affiliations

  1. Russian Science Center Kurchatov Institute, Moscow, Russia

    Yu. Yu. Kloss

  2. Dorodnitsyn Computing Center, Russian Academy of Sciences, 40 Vavilov St., 119333, Moscow, Russia

    F. G. Cheremisin

  3. Moscow Institute of Physics and Technology (MFTI), 9 Institutskii Pereulok, 141700, Dolgoprudnyi, Moscow Oblast, Russia

    N. I. Khokhlov & B. A. Shurygin

Authors
  1. Yu. Yu. Kloss
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. G. Cheremisin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. I. Khokhlov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. B. A. Shurygin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Atomnaya Énergiya, Vol. 105, No. 4, pp. 211–217, October, 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kloss, Y.Y., Cheremisin, F.G., Khokhlov, N.I. et al. Programming and modelling environment for studies of gas flows in micro- and nanostructures based on solving the Boltzmann equation. At Energy 105, 270–279 (2008). https://doi.org/10.1007/s10512-009-9096-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10512-009-9096-3

Keywords

Search

Navigation