Geodesic
On a diffusion gas model in phase space at moderate Knudsen numbers
Matematičeskoe modelirovanie, Tome 24 (2012) no. 8, pp. 45-64.

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

Verification of a gas meso-model, described by the system of stochastic differential equations or Kolmogorov–Fokker–Planck type equation, is represented by the example of space homogenous relaxation.
Keywords: Boltzmann equation, Navier–Stokes equations, stochastic differential equations with respect to Poisson and Wiener measures.
Mots-clés : Kolmogorov–Fokker–Planck equations, quasigasdynamics equations 
@article{MM_2012_24_8_a2,
     author = {S. V. Bogomolov and I. G. Gudich},
     title = {On a diffusion gas model in phase space at moderate {Knudsen} numbers},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {45--64},
     publisher = {mathdoc},
     volume = {24},
     number = {8},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2012_24_8_a2/}
}
TY  - JOUR
AU  - S. V. Bogomolov
AU  - I. G. Gudich
TI  - On a diffusion gas model in phase space at moderate Knudsen numbers
JO  - Matematičeskoe modelirovanie
PY  - 2012
SP  - 45
EP  - 64
VL  - 24
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2012_24_8_a2/
LA  - ru
ID  - MM_2012_24_8_a2
ER  - 
%0 Journal Article
%A S. V. Bogomolov
%A I. G. Gudich
%T On a diffusion gas model in phase space at moderate Knudsen numbers
%J Matematičeskoe modelirovanie
%D 2012
%P 45-64
%V 24
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2012_24_8_a2/
%G ru
%F MM_2012_24_8_a2
S. V. Bogomolov; I. G. Gudich. On a diffusion gas model in phase space at moderate Knudsen numbers. Matematičeskoe modelirovanie, Tome 24 (2012) no. 8, pp. 45-64. http://geodesic.mathdoc.fr/item/MM_2012_24_8_a2/

[1] A. V. Skorokhod, Stokhasticheskie uravneniya dlya slozhnykh sistem, Nauka, M., 1983 | MR

[2] A. A. Arsenev, “O priblizhenii resheniya uravneniya Boltsmana resheniyami stokhasticheskikh differentsialnykh uravnenii Ito”, Zhurnal vychisl. matem. i matem. fiziki, 27:3 (1987), 400–410 | MR

[3] S. V. Bogomolov, “Ob odnom podkhode k polucheniyu stokhasticheskikh modelei gazodinamiki”, DAN, 423:4 (2008), 458–461 | MR

[4] S. V. Bogomolov, “Uravnenie Fokkera–Planka dlya gaza pri umerennykh chislakh Knudsena”, Matematicheskoe modelirovanie, 15:4 (2003), 16–22 | MR | Zbl

[5] S. V. Bogomolov, “O modeli Fokkera–Planka dlya integrala stolknovenii Boltsmana pri umerennykh chislakh Knudsena”, Matematicheskoe modelirovanie, 21:1 (2009), 111–117 | MR | Zbl

[6] S. V. Bogomolov, L. V. Dorodnitsyn, “Uravnenie stokhasticheskoi kvazigazodinamiki. Sluchai vyazkogo gaza”, Matematicheskoe modelirovanie, 22:12, 49–64 | MR | Zbl

[7] Cherchinyani K., Teoriya i prilozheniya uravneniya Boltsmana, Mir, M., 1978 | MR

[8] S. Chandrasekhar, “Stochastic Problems in Physics and Astronomy”, Rev. Modern. Phys., 15:1 (1943), 1 | DOI | MR | Zbl

[9] J. G. Kirkwood, “The Statistical Mechanical Theory of Transport Processes”, J. Chem. Phys., 14:3 (1946), 180 | DOI

[10] E. M. Shakhov, V. A. Titarev, “Approksimatsiya uravneniya Boltsmana i kineticheskie modeli”, Entsiklopediya nizkotemperaturnoi plazmy, Ser. B, v. VII-1/3, Matematicheskoe modelirovanie v nizkotemperaturnoi plazme, ed. V. E. Fortov, Yanus-K, M., 2008, 79–100

[11] V. V. Aristov, S. A. Zabelok, “A deterministic method for solving the Boltzmann equation with parallel computations”, Zh. Vychisl. Mat. Mat. Fiz., 42:3 (2002), 425–437 | MR | Zbl

[12] P. Asinari, “Nonlinear Boltzmann equation for the homogeneous isotropic case: Minimal deterministic Matlab program”, Comput. Phys. Commun., 181 (2010), 1776 | DOI | MR | Zbl

[13] An. V. Lukshin, S. N. Smirnov, “Ob odnom stokhasticheskom metode resheniya uravneniya Boltsmana”, Zhurnal vychisl. matem. i matem. fiziki, 28:2 (1988), 293–298 | MR

[14] B. A. Trubnikov, “Stolknoveniya chastits v polnostyu ionizovannoi plazme”, Voprosy teorii plazmy, 1, Gosatomizdat, M., 1963, 98–182

[15] Berd G., Molekulyarnaya gazovaya dinamika, Mir, M., 1981

[16] S. V. Bogomolov, “Uravneniya kvazigazodinamiki”, Matematicheskoe modelirovanie, 21:12 (2009), 145–151 | Zbl

[17] P. Jenny, M. Torrilhon, S. Heinz, “A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion”, J. of Comp. Phys., 2010, no. 229, 1077–1098 | DOI | MR | Zbl