**AUTHORS:**Yu. A. Nikitchenko, S. A. Popov, A. V. Tikhonovets

**Download as PDF**

**ABSTRACT:**
A mathematical model of the flow of a polyatomic gas containing a combination of the NavierStokes-Fourier model (NSF) and the model kinetic equation of polyatomic gases is presented. At the heart of
the composed components is a unified physical model, as a result of which the NSF model is a strict first
approximation of the model kinetic equation. The model allows calculations of flow fields in a wide range of
Knudsen numbers ( Kn ), as well as fields containing regions of high dynamic nonequilibrium. The boundary
conditions on a solid surface are set at the kinetic level, which allows, in particular, to formulate the boundary
conditions on the surfaces absorbing or emitting gas. The composed model was tested. The example of the
problem of the shock wave profile shows that up to Mach numbers M 2 the combined model gives smooth
solutions even in those cases where the sewing point is in a high gradient region. For the Couette flow, smooth
solutions are obtained at M 5, Kn 0.2 . As a result of research, a weak and insignificant difference
between the kinetic region of the composed model and the “pure” kinetic model was established. A model
effect was discovered: in the region of high nonequilibrium, there is an almost complete coincidence of the
solutions of the kinetic region of the combined model and the “pure” kinetic solution.
This work was conducted with the financial support of the Ministry of Education and Science of the Russian
Federation, project №9.7170.2017/8.9.

**KEYWORDS:**
polyatomic gases, Navier-Stokes-Fourier model, model kinetic equation, composed model,
dynamic nonequilibrium, sorption surfaces.

**REFERENCES:**

[
1] P. Degond, S. Jin, L. Mieussens, A smooth
transition model between kinetic and hydrodynamic
equations, Journal of Computational Physics,
No.209, 2005, pp. 665–694.

[2] I.V. Egorov, A.I. Erofeev, Continuum and
kinetic approaches to the simulation of the
hypersonic flow past a flat plate, Fluid Dynamics,
Volume 32, Issue 1, January 1997, pp 112–122.

[3] G. Abbate, C.R. Kleijn, B.J. Thijsse, Hybrid
continuum/molecular simulations of transient gas
flows with rarefaction, AIAA Journal, Vol. 47, No.
7, 2009, pp. 1741-1749.

[4] N. Crouseilles, P. Degond, M. Lemou, A
hybrid kinetic-fluid model for solving the gas
dynamics Boltzmann-BGK equations, J. Comput.
Phys., 199, 2004, pp 776-808.

[5] N. Crouseilles, P. Degond, M. Lemou, A
hybrid kinetic-fluid model for solving the VlasovBGK equations, Journal of Computational Physics,
203, 2005, pp 572-601.

[6] E.M. Shakhov, Metod issledovaniia dvizhenii
razrezhennogo gaza, М.: Nauka, 1975. 207 s.

[7] O.I. Rovenskaya, G. Croce, Numerical
simulation of gas flow in rough micro channels:
hybrid kinetic–continuum approach versus Navier–
Stokes, Microfluid Nanofluid, 2016, 20:81.

[8] Yu.A. Nikitchenko, Model Kinetic Equation
for Polyatomic Gases, Computational Mathematics
and Mathematical Physics, Volume 57, Issue 11,
November 2017, pp 1843–1855.

[9] Yu.A. Nikitchenko, Modeli neravnovesnykh
techenii, М.: Izd-vo MAI, 2013. 160 s.

[10] V.A. Rykov, A model kinetic equation for a gas
with rotational degrees of freedom, Fluid Dynamics,
Volume 10, Issue 6, November 1975, pp 959–966.

[11] I.N. Larina, V.A. Rykov, Kinetic model of the
Boltzmann equation for a diatomic gas with
rotational degrees of freedom, Computational
Mathematics and Mathematical Physics, Volume
50, Issue 12, December 2010, pp 2118–2130

[12] H. Alsmeyer, Density profiles in argon and
nitrogen shock waves measured by the absorption of
an electron beam, J. Fluid Mech., V. 74, Pt. 3, 1976,
pp. 497-513.

[13] F. Robben, L. Talbot, Experimental study of
the rotational distribution function of nitrogen in a
shock wave, Phys. Fluids, V. 9, № 4, 1966, pp. 653-
662.

[14] V.S. Glinkina, Yu.A. Nikitchenko, S.A. Popov,
Yu.A. Ryzhov, Drag Coefficient of an Absorbing
Plate Set Transverse to a Flow, Fluid Dynamics,
November 2016, Volume 51, Issue 6, pp 791–798.

[15] A.I. Erofeev. Investigation of the Nitrogen
Shock Wave Structure on the Basis of Trajectory
Calculations of the Molecular Interaction, Fluid
Dynamics, Volume 37, Issue 6, November 2002, pp
970–982.

[16] Elizarova T.G., Khokhlov A.A., Montero S.,
Numerical simulation of shock wave structure in
nitrogen, Physics of Fluids, vol.19 (N 6) 068102,
2007.

[17] M.E. Berezko, Yu.A. Nikitchenko, A.V.
Tikhonovets, Sshivanie kineticheskoi i
gidrodinamicheskoi modelei na primere techeniya
Kuetta, Trudy MAI, Vyp.№94,
http://trudymai.ru/published.php?ID=80922