Application of the Conservative Splitting Method for Investigating Near Continuum Gas Flows

  • V. V. Aristov
Part of the Fluid Mechanics and its Applications book series (FMIA, volume 60)

Abstract

The principal of the hydrodynamic conservativity (the hydrodynamic compliance) as mentioned in is the basis of constructing the conservative splitting method (CSM), and this approach results in a natural and truly description of a flow by means of the macroscopic equation. It is also valid for near continuum regimes considered by means of the kinetic equation. Generally speaking, it is possible to describe such flows using the same spatial steps (less than the characteristic free path) as for flows at moderate Knudsen numbers. However, for these flow regimes the requirements on computer resources are severe and increase at least proportionally to the inverse Knudsen number.

Keywords

Entropy Lution Boris 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bishaev A.M., Rykov V.A. (1975) Solution of steady problems of the kinetic theory of gases at moderate and small Knudsen numbers, USSR Journ. Comp. Math. Math. Phys., Vol. no. 15, pp. 172–182.MATHGoogle Scholar
  2. 2.
    Bishaev A.M., Rykov V.A. (1978) Condensation of monatomic gas at small Knudsen numbers, USSR Journ. Comp. Math. Math. Phys., Vol. no. 18, pp. 709–717.MATHGoogle Scholar
  3. 3.
    Demina E.N., Rykov V.A. (1986) Method of numerical analysis of subsonic rarefied gas flows at small Knudsen numbers, Doklady Akad. Nauk SSSR, Vol. no. 291, pp. 793–797.Google Scholar
  4. 4.
    Aristov V.V., Tcheremissine F.G. (1982) The kinetic numerical method for rarefied and continuum gas flows. Book of Abstracts of 13-th Intern. Symp. on Rarefied Gas Dynamics, Novosibirsk, Vol. no. 1, pp. 147–149. (see also: (1985) Rarefied Gas Dynamics, New York, Plenum Press, Vol.1, pp. 269-276).Google Scholar
  5. 5.
    Aristov V.V., Tcheremissine F.G. (1983) Solving the Euler and Navier-Stokes equations on the basis of the splitting operator of the kinetic equation, Doclady Acad. Nauk SSSR, Vol. no. 272, pp. 555–559.ADSGoogle Scholar
  6. 6.
    Lengrand J.-C, Raffin M., Allegre J. (1981) Monte-Carlo simulation method applied to jet-wall interaction under continuum flow conditions. Progress in Astronaut and Aeronaut, Vol. no. 74, pp. 994–1006.Google Scholar
  7. 7.
    Pullin D.I. (1980) Direct simulation methods for compressible inviscid ideal-gas flow, J. Comput. Phys., Vol. no. 34, pp. 231–244.ADSMATHCrossRefGoogle Scholar
  8. 8.
    Reitz R.D. (1981) One-dimensional compressible gasdynamics calculations using the Boltzmann equation, J. Comput. Phys., Vol. no. 42, pp. 108–123.ADSMATHCrossRefGoogle Scholar
  9. 9.
    Potkin V.V. (1975) Kinetic analysis of different schemes for gasdynamics USSR Journ. Comp. Math. Math. Phys., Vol. no. 15, pp. 1493–1498.MathSciNetGoogle Scholar
  10. 10.
    Kaniel S., Falcovitz J. (1980) Transport approach for compressible flow. Comput. meth.in applied sci.and engineering, R. Glowinsky and J.L. Lions eds., INRIA, pp. 135–151.Google Scholar
  11. 11.
    Elizarova T.G., Chetverushkin B.N. (1984) About the numerical algorithm for calculating gasdynamic flows Doclady Acad. Nauk SSSR, Vol. no. 279, pp. 80–83.ADSGoogle Scholar
  12. 12.
    Elizarova T.G., Chetverushkin B.N. (1985) Kinetic algorithms for calculating gasdynamic flows USSR Journ. Comp. Math. Math. Phys., Vol. no. 25, pp. 1526–1533.MathSciNetGoogle Scholar
  13. 13.
    Deshpande S.M. (1986) Kinetic theory based new upwind methods for inviscid compressible flowsm, A1AA. Paper 86–0275.Google Scholar
  14. 14.
    Godunov S.K. (1957) Difference method of computing shock waves. Uspehi matematicheskih nauk, Vol. no. 12, pp. 176–177.MathSciNetMATHGoogle Scholar
  15. 15.
    Boris J.P., Book D.L. (1973) Flux corrected transport. I. SHASTA. A fluid transport algorithm that works. J. Comput. Phys., Vol. no. 11, pp. 38–69.ADSMATHCrossRefGoogle Scholar
  16. 16.
    Rozhdestveskii B.N., Janenko N.N. (1969) Systems of quasilinear equations. Novosibirsk, Nauka.Google Scholar
  17. 17.
    Harlow F. (1964) The Particle-In-Cell computing method for fluid dynamics. Methods in Computational Physics, Vol. no. 3, pp. 319–345.Google Scholar
  18. 18.
    Hicks B.L., Yen S.M., Reilly B.J. (1972) The internal structures of shock waves, J. Fluid Mech., Vol. no. 53, pp.85–111.ADSMATHCrossRefGoogle Scholar
  19. 19.
    Beylich A. (1999) Numerical modules for solving the Boltzmann equation in the transition regime. Rarefied Gas Dynamics, Brun R. et al. eds., Cepadues-Editions, Toulouse, Vol. no. 2, pp. 197–204.Google Scholar
  20. 20.
    Nelson D.A., Doo Y.C. (1989) Simulation of multicomponent nozzle flows into a vacuum, Progr.in Astronaut and Aeronaut, Vol. no. 116, pp. 340–351.ADSGoogle Scholar
  21. 21.
    Teshima K., Usami M. Caracteristics of supersonic jet flows and DSMC analysis, Rarefied Gas Dynamics, Shen C. ed., Peking University Press, pp. 387–394.Google Scholar
  22. 22.
    Erofeev A.I., Belotserkovskii O.M., Janitskii V.E. (1980) Direct statistical simulation of the rarefied gas flows. Proc. 6th All-Union Conf. on Raref. Gas Dynam., Novosibirsk, Part. 2, pp. 2–12.Google Scholar
  23. 23.
    Starikov B.B. Normal and tangent stresses on a plate in a flow of rarefied gas. Proc. 6th All-Union Conf. on Raref. Gas Dynam., Novosibirsk, Part.2, pp. 98–103.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • V. V. Aristov
    • 1
  1. 1.Computing Center of the Russian Academy of SciencesMoscowRussia

Personalised recommendations