VV-exchange in direct Monte Carlo simulation of rarefied gas flows



direct simulation Monte Carlo method, VV-exchange, RT-exchange, VT-exchange, Larsen-Borgnakke model


A question of modeling of vibration-vibration (VV) exchange in calculation of rarefied gas flows by the direct simulation Monte Carlo method is considered. Two simple models for VV-exchange in collisions of simple harmonic oscillator molecules are proposed: a model with single-quantum transitions and an extension of the Larsen-Borgnakke model used widely for RT- and VT-exchange. Computation of vibrational relaxation is performed for homogeneous test conditions and for the conditions of an experiment on vibrational population evolution in nitrogen excited vibrationally by a laser. The numerical results obtained are in good agreement with experimental data.

Author Biographies

Ye.A. Bondar

S.F. Gimelshein

Novosibirsk State University
• Head of Laboratory

A.N. Molchanova

Novosibirsk State University,
Department of Mathematics and Mechanics,
ул. Пирогова, 1, 630090, Новосибирск
• PhD Student

M.S. Ivanov


  1. Bird G.A. Molecular gas dynamics and the direct simulation of gas flows. Oxford: Clarendon Press, 1994.
  2. Borgnakke C., Larsen P.S. Statistical collision model for Monte Carlo simulation of polyatomic gas mixture // J. Comput. Phys. 1975. 18, N 4. 405-420.
  3. Haas B.L., Hash D.B., Bird G.A., Lumpkin F.E., Hassan H.A. Rates of thermal relaxation in direct simulation Monte Carlo methods // Phys. Fluids. 1994. 6, N 6. 2191-2201.
  4. Gimelshein N.E., Gimelshein S.F., Levin D.A. Vibrational relaxation rates in the direct simulation Monte Carlo method // Phys. Fluids. 2002. 14, N 12. 4452-4455.
  5. Rapp D., Englander-Golden P. Resonant and near-resonant vibrational-vibrational energy transfer between molecules in collisions // J. Chem. Phys. 1964. 40, N 2. 573-575.
  6. Morse R.I. Semiclassical transition probabilities for collinear diatom-diatom collisions // J. Chem. Phys. 1972. 56, N 5. 2329-2332.
  7. Billing G.D., Fisher E.R. V-V and V-T rate. Coefficients in N_2 by a quantum-classical model // J. Chem. Phys. 1979. 43, N 3. 395-401.
  8. Bogdanov A.V., Dubrovskii G.V., Gorbachev Yu.E., Strelchenya V.M. Theory of vibrational and rotational excitation of polyatomic molecules // Phys. Rep. 1989. 181, N 3. 121-206.
  9. Adamovich I.V. Three-dimensional analytic model of vibrational energy transfer in molecule-molecule collisions // AIAA J. 2001. 39, N 10. 1916-1925.
  10. Koura K. Improved null-collision technique in the direct simulation Monte Carlo method: application to vibrational relaxation of nitrogen // Comp. Math. Appl. 1998. 35, N 1/2. 139-154.
  11. Abe T. Inelastic collision model for vibrational-translational and vibrational-vibrational energy transfer in the direct simulation Monte Carlo method // Phys. Fluids. 1994. 6, N 9. 3175-3179.
  12. Haas B.L. Thermochemistry models applicable to a vectorized particle simulation. Ph.D. thesis. Stanford University. Stanford, 1990.
  13. Bruno D., Capitelli M., Longo S., Minelli P., Taccogna F. Particle kinetic modelling of rarefied gases and plasmas // Plasma Sources Sci. Technol. 2003. 12, N 4. S89-S97.
  14. Gimelshein S.F., Ivanov M.S., Markelov G.N., Gorbachev Yu.E. Quasiclassical VRT transitional models in the DSMC computations of reacting flows // Proc. 20th Int. Symp. on Rarefied Gas Dynamics. Beijing: Peking Univ. Press, 1997. 711-717.
  15. Gimelshein S.F., Ivanov M.S., Markelov G.N., Gorbachev Yu.E. Statistical simulation of nonequilibrium rarefied flows with quasiclassical energy transfer models // J. Thermophys. Heat Transfer. 1998. 12, N 4. 2079-2086.
  16. Gimelshein S.F., Boyd I.D., Sun Q., Ivanov M.S. DSMC modeling of vibration-translation energy transfer in hypersonic rarefied flows // AIAA Paper 99-3451. 1999.
  17. Ahn T., Adamovich I.V., Lempert W.R. Determination of nitrogen V-V transfer rates by stimulated Raman pumping // Chem. Phys. 2004. 298, N 1-3. 233-240.
  18. Scwartz R.N., Slawsky Z.I., Herzfeld K.F. Calculation of vibrational relaxation times in gases // J. Chem. Phys. 1952. 20, N 10. 1591-1599.
  19. Chernyi G.G., Losev S.A., Macheret S.O., Potapkin B.V. Physical and chemical processes in gas dynamics: cross sections and rate constants. Vol. I. Reston: American Institute of Aeronautics and Astronautics, 2002.
  20. Ivanov M.S., Markelov G.N., Gimelshein S.F. Statistical simulation of reactive rarefied flows: numerical approach and applications // AIAA Paper 98-2669. 1998.
  21. Bondar Ye., Gimelshein N., Gimelshein S., Ivanov M., Wysong I. On the accuracy of DSMC modeling of rarefied flows with real gas effects // AIP Conf. Proc. 2005. 762. 607-613.



How to Cite

Бондарь Е.А., Гимельшейн С.Ф., Молчанова А.Н., Иванов М.С. VV-Exchange in Direct Monte Carlo Simulation of Rarefied Gas Flows // Numerical methods and programming. 2014. 15. 549-559



Section 1. Numerical methods and applications