On Fokker--Planck model for Boltzmann collision integral at moderate Knudsen numbers
Matematičeskoe modelirovanie, Tome 21 (2009) no. 1, pp. 111-117.

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

Explicit approximate coefficients in the Fokker–Planck equation in the phase space for modeling a gas of rigid spheres at transient (from kinetic to macroscopic description) Knudsen numbers are obtained.
@article{MM_2009_21_1_a8,
     author = {S. V. Bogomolov},
     title = {On {Fokker--Planck} model for {Boltzmann} collision integral at moderate {Knudsen} numbers},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {111--117},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2009_21_1_a8/}
}
TY  - JOUR
AU  - S. V. Bogomolov
TI  - On Fokker--Planck model for Boltzmann collision integral at moderate Knudsen numbers
JO  - Matematičeskoe modelirovanie
PY  - 2009
SP  - 111
EP  - 117
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2009_21_1_a8/
LA  - ru
ID  - MM_2009_21_1_a8
ER  - 
%0 Journal Article
%A S. V. Bogomolov
%T On Fokker--Planck model for Boltzmann collision integral at moderate Knudsen numbers
%J Matematičeskoe modelirovanie
%D 2009
%P 111-117
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2009_21_1_a8/
%G ru
%F MM_2009_21_1_a8
S. V. Bogomolov. On Fokker--Planck model for Boltzmann collision integral at moderate Knudsen numbers. Matematičeskoe modelirovanie, Tome 21 (2009) no. 1, pp. 111-117. http://geodesic.mathdoc.fr/item/MM_2009_21_1_a8/

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

[2] C. Cercignani, Rarefied Gas Dynamics, Cambridge University Press, 2000 | MR | Zbl

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

[4] B. N. Chetverushkin, Kineticheski-soglasovannye skhemy v gazovoi dinamike, Izd-vo Mos. un-ta, M., 1999

[5] N. B. Maslova, Nonlinear Evolution Equations. Kinetic Approach, World Scientific Publishing Co. Pte. Ltd., 1993 | MR | Zbl

[6] L. D. Landau, “Kineticheskoe uravnenie v sluchae kulonovskogo vzaimodeistviya”, ZhETF, 7:2 (1937), 203–209 | Zbl

[7] J. G. Kirkwood, “The Statistical Mechanical Theory of Transport Processes”, J. Chem. Phys., 14:3 (1946), 180–201 | DOI

[8] S. Chandrasekhar, “Stochastic Problems in Physics and Astronomy”, Rev. Modern. Phys., 15:1 (1943), 1–89 | DOI | MR | Zbl

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

[10] S. G. Rautian, “Diffuzionnoe priblizhenie v zadache o migratsii chastits v gaze”, Uspekhi fizicheskikh nauk, 161:11 (1991), 151–170

[11] Yu. L. Klimontovich, “O neobkhodimosti i vozmozhnosti edinogo opisaniya kineticheskikh i gidrodinamicheskikh protsessov”, Teor. i matem. fizika, 92:2 (1992), 312–330 | MR | Zbl

[12] A. A. Arsenev, O. E. Buryak, “O svyazi mezhdu resheniem uravneniya Boltsmana i resheniem uravneniya Landau–Fokkera–Planka”, Matematicheskii sbornik, 181:4 (1990), 435–446 | MR | Zbl

[13] A. A. Arsenev, Lektsii o kineticheskikh uravneniyakh, Nauka, M., 1992 | MR

[14] O. E. Lanford III, “O vyvode uravneniya Boltsmana”, Neravnovesnye yavleniya: uravnenie Boltsmana, eds. Dzh. L. Libovits, E. U. Montroll, Mir, M., 1986 | MR

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

[16] V. S. Korolyuk, N. I. Portenko, A. V. Skorokhod, A. F. Turbin, Spravochnik po teorii veroyatnostei i matematicheskoi statistike, Nauka, M., 1985 | MR | Zbl

[17] C. Villani, A Review of Mathematical Topics in Collisional Kinetic Theory, Handbook of Mathematical Fluid Dynamics, Vol. 1, Elsevier Science, 2002 ; http://www.umpa.ens-lyon.fr/~cvillani/surveys.html | MR | Zbl

[18] A. Lukschin, H. Neunzert, J. Struckmeier, “Coupling of Navier–Stokes and Boltzmann Regions”, HERMES Aerodynamics R/Q Program meeting, VKI, 1992

[19] A. V. Lukshin, S. N. Smirnov, “Ob odnom effektivnom stokhasticheskom algoritme resheniya uravneniya Boltsmana”, Zhurnal vychisl. matem. i matem. fiziki, 29:1 (1989), 118–124 | MR | Zbl

[20] H. Babovsky, “On a Simulation Scheme for the Boltzmann Equation”, Math. Meth. in the Appl. Sci., 8 (1986), 223–233 | DOI | MR | Zbl

[21] V. I. Kolobov, R. R. Arslanbekov, V. V. Aristov, A. A. Frolova, S. A. Zabelok, “Unified Solver for Rarefied and Continuum Flows with Adaptive Mesh and Algorithm Refinement”, Journal of Computational Physics, 223 (2007), 589–608 | DOI | Zbl

[22] K. Morinishi, “A Continuum/Kinetic Hybrid Approach for Multi-Scale Flow Simulation”, European Conference on Computational Fluid Dynamics ECCOMAS CFD, TU Delft, the Netherlands, 2006

[23] V. A. Titarev, “Conservative numerical methods for model kinetic equations”, Computers and Fluids, 36:9 (2007), 1446–1459 | DOI | MR

[24] P. Degond, M. Lemou, “Turbulence models for incompressible fluids derived from kinetic theory”, J. Math. Fluid Mech., 4:3 (2002), 257–284 | DOI | MR | Zbl

[25] T. G. Elizarova, Kvazigidrodinamicheskie uravneniya i metody rascheta vyazkikh techenii, Nauchnyi mir, M., 2007

[26] S. V. Bogomolov, “Stokhasticheskaya model gidrodinamiki”, Matematicheskoe modelirovanie, 2:11 (1990), 85–88 | MR | Zbl

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