Quasigasdynamic system of equations and Navier--Stokes equations
Matematičeskoe modelirovanie, Tome 16 (2004) no. 4, pp. 98-104.

Voir la notice de l'article provenant de la source Math-Net.Ru

The connection between the unsteady quasigasdynamic system of equations and Navier–Stokes equations is considered. It is shown that in the case of the low natural dissipative terms the difference between these systems is about $O(\tau^2)$, where $\tau$ is the typical short time between molecula collisions.
@article{MM_2004_16_4_a10,
     author = {K. N. Ivanova and B. N. Chetverushkin and N. G. Churbanova},
     title = {Quasigasdynamic system of equations and {Navier--Stokes} equations},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {98--104},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_4_a10/}
}
TY  - JOUR
AU  - K. N. Ivanova
AU  - B. N. Chetverushkin
AU  - N. G. Churbanova
TI  - Quasigasdynamic system of equations and Navier--Stokes equations
JO  - Matematičeskoe modelirovanie
PY  - 2004
SP  - 98
EP  - 104
VL  - 16
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2004_16_4_a10/
LA  - ru
ID  - MM_2004_16_4_a10
ER  - 
%0 Journal Article
%A K. N. Ivanova
%A B. N. Chetverushkin
%A N. G. Churbanova
%T Quasigasdynamic system of equations and Navier--Stokes equations
%J Matematičeskoe modelirovanie
%D 2004
%P 98-104
%V 16
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2004_16_4_a10/
%G ru
%F MM_2004_16_4_a10
K. N. Ivanova; B. N. Chetverushkin; N. G. Churbanova. Quasigasdynamic system of equations and Navier--Stokes equations. Matematičeskoe modelirovanie, Tome 16 (2004) no. 4, pp. 98-104. http://geodesic.mathdoc.fr/item/MM_2004_16_4_a10/

[1] M. I. Volchinskaya, A. N. Pavlov, B. N. Chetverushkin, Ob odnoi skheme integrirovaniya uravnenii gazovoi dinamiki, Preprint No 113, IPM im. M. V. Keldysha AN SSSR, M., 1983, 12 pp. | MR

[2] B. N. Chetverushkin, Kineticheski-soglasovannye skhemy v gazovoi dinamike, Izd-vo MGU, M., 1999, 232 pp.

[3] T. G. Elizarova, B. N. Chetverushkin, “Ispolzovanie kineticheskikh modelei dlya rascheta gazodinamicheskikh techenii”, Mat. modelirovanie, 1986, 261–278 | MR

[4] L. W. Dorodnycyn, B. N. Chetverushkin, “The simulation of unsteady and transitional viscous compressible das flows on multiprocessor systems”, Computational Fluid Dynamics Journal (Japan Soc. of CFD Journal), 11:2 (2002), 186–194

[5] I. A. Graur, M. S. Ivanov, G. N. Markelov, Y. Burtschell, E. Valerio, D. Zeitoun, “Comparision of kinetic and continuum approaches for simulation of shok wave/boundary layer interaction”, Proceedings of 23 int Symp. Of Shok Waves, Texas, USA, 2001, 2916

[6] Yu. V. Sheretov, Uravneniya Nave-Stoksa kak asimptotika obobschennoi kvazigazodinamicheskoi sistemy, Preprint No 46, IPM im. Keldysha AN SSSR, 1990, 12 pp. | MR

[7] V. F. Kovalev, B. N. Chetverushkin, “Ob invariantnosti kvazigazodinamicheskoi sistemy uravnenii”, Doklady RAN, 388:6 (2003), 743–746 | MR | Zbl

[8] D. E. Machin, B. N. Chetverushkin, “Kineticheskie i Lattice Boltzmann skhemy”, Matematicheskoe modelirovanie, 16:3 (2004), 87–94 | MR | Zbl

[9] Succi S., The Lattice Boltzmann equations, Claredon Press, Oxford, 2001, 288 pp. | MR | Zbl

[10] R. Libov, Vvedenie v teoriyu kineticheskikh uravnenii, Mir, M., 1974, 371 pp.

[11] K. Cherchinyani, “O metodakh resheniya uravneniya Boltsmana”, Neravnovesnye yavleniya: Uravneniya Boltsmana, eds. Dzh. L. Libovits, E. U. Montropp, Mir, M., 1986, 132–204 | MR

[12] U. Ghia, K. N. Ghia, C. T. Shin C. T., “High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method”, J. Comput. Phys., 48:3 (1982), 387–411 | DOI | Zbl