Simulation of rarefied gas flows on the basis of the Boltzmann kinetic equation solved by applying a conservative projection method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 6, pp. 1008-1024
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Flows of a simple rarefied gas and gas mixtures are computed on the basis of the Boltzmann kinetic equation, which is solved by applying various versions of the conservative projection method, namely, a two-point method for a simple gas and gas mixtures with a small difference between the molecular masses and a multipoint method in the case of a large mass difference. Examples of steady and unsteady flows are computed in a wide range of Mach and Knudsen numbers.
@article{ZVMMF_2016_56_6_a7,
     author = {O. I. Dodulad and Yu. Yu. Kloss and A. P. Potapov and F. G. Tcheremissine and P. V. Shuvalov},
     title = {Simulation of rarefied gas flows on the basis of the {Boltzmann} kinetic equation solved by applying a conservative projection method},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1008--1024},
     year = {2016},
     volume = {56},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a7/}
}
TY  - JOUR
AU  - O. I. Dodulad
AU  - Yu. Yu. Kloss
AU  - A. P. Potapov
AU  - F. G. Tcheremissine
AU  - P. V. Shuvalov
TI  - Simulation of rarefied gas flows on the basis of the Boltzmann kinetic equation solved by applying a conservative projection method
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2016
SP  - 1008
EP  - 1024
VL  - 56
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a7/
LA  - ru
ID  - ZVMMF_2016_56_6_a7
ER  - 
%0 Journal Article
%A O. I. Dodulad
%A Yu. Yu. Kloss
%A A. P. Potapov
%A F. G. Tcheremissine
%A P. V. Shuvalov
%T Simulation of rarefied gas flows on the basis of the Boltzmann kinetic equation solved by applying a conservative projection method
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2016
%P 1008-1024
%V 56
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a7/
%G ru
%F ZVMMF_2016_56_6_a7
O. I. Dodulad; Yu. Yu. Kloss; A. P. Potapov; F. G. Tcheremissine; P. V. Shuvalov. Simulation of rarefied gas flows on the basis of the Boltzmann kinetic equation solved by applying a conservative projection method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 6, pp. 1008-1024. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a7/

[1] Belotserkovskii O. M., Yanitskii V. E., “Statisticheskii metod chastits yacheikakh dlya resheniya zadach dinamiki razrezhennogo gaza. 1. Osnovy postroeniya metoda”, Zh. vychisl. matem. i matem. fiz., 15:5 (1975), 1195–1208 | MR | Zbl

[2] Nordsieck A., Hicks B. L., “Monte Carlo evaluation of the Boltzmann collision integral”, Rarefied Gas Dynamics, 1 (1967), 695–710

[3] Aristov V. V., Cheremisin F. G., “Konservativnyi metod rasschepleniya dlya resheniya uravneniya Boltsmana”, Zh. vychisl. matem. i matem. fiz., 21:1 (1980), 208–225

[4] Tcheremissine F. G., “Conservative discrete ordinates method for solving Boltzmann kinetic equation”, Commun. Appl. Mathem., Russian Acad. Sci. Comput. Center, M., 1996, 50

[5] Cheremisin F. G., “Konservativnyi metod vychisleniya integrala stolknovenii Boltsmana”, Dokl. RAN, 357:1 (1997), 53–56

[6] Cheremisin F. G., “Reshenie uravneniya Boltsmana pri perekhode k gidrodinamicheskomu rezhimu techeniya”, Dokl. RAN, 373:4 (2000), 483–486

[7] Cheremisin F. G., “Reshenie kineticheskogo uravneniya Boltsmana dlya vysokoskorostnykh techenii”, Zh. vychisl. matem. i matem. fiz., 46:2 (2006), 329–343 | MR

[8] Raines A. A., “Metod resheniya uravneniya Boltsmana dlya smesi gazov v sluchae tsilindricheskoi simmetrii v prostranstve skorostei”, Zh. vychisl. matem. i matem. fiz., 42:8 (2002), 1258–1269 | MR | Zbl

[9] Dodulad O. I., Tcheremissine F. G., “Multipoint conservative projection method for computing the Boltzmann collision integral for gas mixtures”, 28th Internat. Symposium on Rarefied Gas Dynamics, AIP Conf. Proc., 1501, 2012, 302–309 | DOI

[10] Cheremisin F. G., “Reshenie kineticheskogo uravneniya Boltsmana dlya mnogoatomnogo gaza”, Zh. vychisl. matem. i matem. fiz., 52:2 (2012), 270–287 | MR | Zbl

[11] Anikin Yu. A., Dodulad O. I., “Reshenie kineticheskogo uravneniya dlya dvukhatomnogo gaza s ispolzovaniem differentsialnykh sechenii rasseyaniya, rasschitannykh metodom klassicheskikh traektorii”, Zh. vychisl. matem. i matem. fiz., 53:7 (2013), 1193–1211 | DOI | MR | Zbl

[12] Aristov V. V., Cheremisin F. G., “Rasscheplenie neodnorodnogo kineticheskogo operatora uravneniya Boltsmana”, Dokl. AN SSSR, 231:1 (1976), 49–52 | MR | Zbl

[13] Bobylev A. V., Ohwada T., “On the generalization of Strang's splitting scheme”, Riv. Math. Univ. Parma, 6:2 (1999), 235–243 | MR | Zbl

[14] Korobov N. M., Teoretiko-chislovye metody v priblizhennom analize, Fizmatgiz, M., 1963

[15] Anikin Y. A., Dodulad O. I., Kloss Y. Y., Martynov D. V., Shuvalov P. V., Tcheremissine F. G., “Development of applied software for analysis of gas flows in vacuum devices”, Vacuum, 86:11 (2012), 1770–1777 | DOI

[16] Bazhenov I. I., Dodulad O. I., Ivanova I. D., Kloss Y. Y., Rjabchenkov V. V., Shuvalov P. V., Tcheremissine F. G., “Problem Solving environment for gas flow simulation in micro structures on the base of the Boltzmann equation”, Proc. 13th Intern. Conf. on Math. Meth. Sci. Engny, CMMSE2013 (Spain, 2013), 246–257

[17] Kloss Yu. Yu., Khokhlov N. I., Cheremisin F. G., Shurygin B. A., “Razrabotka chislennykh skhem resheniya kineticheskogo uravneniya v klasternykh sredakh na osnove tekhnologii MPI”, Informatsionnye protsessy, 7:4 (2007), 425–431

[18] Kloss Yu. Yu., Shuvalov P. V., Tcheremissine F. G., “Solving Boltzmann equation on GPU”, ICCS 2010, Proc. Computer Sci., 1, no. 1, 2010, 1077–1085 | DOI

[19] Dodulad O. I., Cheremisin F. G., “Raschety struktury udarnoi volny v odnoatomnom gaze s kontrolem tochnosti”, Zh. vychisl. matem. i matem. fiz., 53:6 (2013), 169–187

[20] Alsmeyer H., “Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam”, J. Fluid. Mech., 74 (1976), 497–513 | DOI

[21] Garen W., Synofzik R., Frohn A., “Shock tube for generation of weak shock waves”, AIAA Journal, 12 (1974), 1132–1134 | DOI

[22] Velikodnyi V. Yu., Emelyanov A. V., Eremin A. V., “Neadiabaticheskoe vozbuzhdenie molekul ioda v zone postupatelnoi neravnovesnosti udarnoi volny”, Zh. teoretich. fiz., 69:10 (1999), 23–33

[23] Dodulad O. I., Kloss Yu. Yu., Cheremisin F. G., “Raschety struktury udarnoi volny s smesi gazov na osnove resheniya uravneniya Boltsmana”, Fiziko-khimicheskaya kinetika v gazovoi dinamike, 14:1 (2013), 1–18

[24] Gmurczyk A. S., Tarczynski M., Walenta Z. A., “Shock wave structure in the binary mixtures of gases with disparate molecular masses”, 11th Intern. Symposium on Rarefied Gas Dynamics, v. 1, 1978, 333–341

[25] Chung C., Wittt K. J. D., Jeng D., Penko P. F., “Internal structure of shock waves in disparate mass mixture”, J. Thermophysic, 7:4 (1993), 742–744 | DOI

[26] Nobuya Miyoshi et al., “Development of ultra small shock tube for high energy molecular beam source”, 26th Int. Symposium on Rarefied Gas Dynamics, AIP Conference Proc., 1084, 2009, 557–562

[27] Kloss Yu. Yu., Cheremisin F. G., Shuvalov P. V., “Reshenie uravneniya Boltsmana dlya nestatsionarnykh techenii s udarnymi volnami v uzkikh kanalakh”, Zh. vychisl. matem. i matem. fiz., 50:6 (2010), 1148–1158 | MR | Zbl

[28] Girshfelder Dzh., Kertis Ch., Berd R., Molekulyarnaya teoriya gazov i zhidkostei, Izd-vo inostr. lit.-ry, M., 1961, 976 pp.

[29] Takata S., Sugimoto H., Kosuge S., “Gas separation by means of the Knudsen compressor”, European J. Mechanics — B/Fluids, 26:2 (2007), 155–181 | DOI | MR | Zbl