Geodesic
Splitting over physical processes as applied to the construction of a numerical method for solving the system of kinetic equations governing a hall thruster rarefied plasma jet
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 10, pp. 1904-1925 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A numerical method is constructed for solving the system of kinetic equations describing the behavior of a rarefied plasma jet exhausted from a Hall thruster. A similar problem was previously considered in the steady case. Now the same problem is solved in the unsteady formulation. The numerical method is based on a generalization of the splitting method with respect to physical processes, which is widely used in rarefied gas dynamics. The basic difficulty faced in the natural generalization of this method as applied to thruster jets is that a boundary condition has to be taken into account when the ion distribution function is determined. This difficulty is overcome by analytically selecting the corresponding term at the stage of free-molecular motion. Another difficulty that can be coped with by the splitting method is that the ion and neutral velocity spaces have widely different scales. Techniques for making the method conservative are described, and situations in which this is necessary are discussed. Qualitative characteristics of some numerical computations are compared with experimental data. The comparison shows that the numerical method constructed adequately reproduces the behavior of the modeled object. 
@article{ZVMMF_2012_52_10_a11,
     author = {A. S. Arkhipov and A. M. Bishaev},
     title = {Splitting over physical processes as applied to the construction of a numerical method for solving the system of kinetic equations governing a hall thruster rarefied plasma jet},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1904--1925},
     year = {2012},
     volume = {52},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_10_a11/}
}
TY  - JOUR
AU  - A. S. Arkhipov
AU  - A. M. Bishaev
TI  - Splitting over physical processes as applied to the construction of a numerical method for solving the system of kinetic equations governing a hall thruster rarefied plasma jet
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2012
SP  - 1904
EP  - 1925
VL  - 52
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_10_a11/
LA  - ru
ID  - ZVMMF_2012_52_10_a11
ER  - 
%0 Journal Article
%A A. S. Arkhipov
%A A. M. Bishaev
%T Splitting over physical processes as applied to the construction of a numerical method for solving the system of kinetic equations governing a hall thruster rarefied plasma jet
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2012
%P 1904-1925
%V 52
%N 10
%U http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_10_a11/
%G ru
%F ZVMMF_2012_52_10_a11
A. S. Arkhipov; A. M. Bishaev. Splitting over physical processes as applied to the construction of a numerical method for solving the system of kinetic equations governing a hall thruster rarefied plasma jet. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 10, pp. 1904-1925. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_10_a11/

[1] Volkov B. I., Morozov A. I., Sveshnikov A. G., Yakunin S. A., “Chislennoe modelirovanie ionov v sisteme s zamknutym dreifom”, Fizika plazmy, 7:2 (1981), 245–253

[2] Zhevandrov P. I., Morozov A. I., Yakunin S. A., “Dinamika plazmy, obrazuyuscheisya pri ionizatsii razrezhennogo gaza”, Fizika plazmy, 10:2 (1984), 353

[3] Bishaev A. M., “Chislennoe modelirovanie strui razreshennogo slabo ionizovannogo gaza, vykhodyaschego iz koltsevogo otverstiya”, Zh. vychisl. matem. i matem. fiz., 33:7 (1993), 1109–1118 | Zbl

[4] Bishaev A. M., Kalashnikov V. K., Kim V., “Chislennoe issledovanie strui razrezhennoi plazmy statsionarnogo uskoritelya s zamknutym dreifom elektronov (UZDP)”, Fizika plazmy, 18:6 (1992), 698–708

[5] Bishaev A. M., Kalashnikov V. K., Kim V., Shavykina A. V., “Chislennoe modelirovanie plazmennoi strui statsionarnogo plazmennogo dvigatelya, rasprostranyayuscheisya v srede nizkogo davleniya”, Fiz. plazmy, 24:11 (1998), 989–995

[6] Arkhipov A. S., Bishaev A. M., “Chislennoe modelirovanie v trekhmernoi postanovke strui plazmy, vykhodyaschei v okruzhayuschee prostranstvo iz statsionarnogo plazmennogo dvigatelya”, Zh. vychisl. matem. i matem. fiz., 47:3 (2007), 490–505 | MR | Zbl

[7] Arkhipov A. S., Bishaev A. M., Kim V., “Vliyanie razlichnykh faktorov na raspredelenie parametrov v strue statsionarnogo plazmennogo dvigatelya”, Matem. modelirovanie, 22:2 (2010), 124–138 | MR

[8] Shakhov E. M., Metod issledovaniya dvizhenii razrezhennogo gaza, Nauka, M., 1974

[9] Larina I. N., Rykov V. A., “Chislennoe reshenie uravneniya Boltsmana metodom simmetrichnogo rasschepleniya”, Zh. vychisl. matem. i matem. fiz., 43:4 (2003), 601–613 | MR | Zbl

[10] Cheremisin F. G., “Reshenie uravneniya Boltsmana pri perekhode k gidrodinamicheskomu rezhimu techeniya”, Dokl. RAN, 373:4 (2000), 479–483

[11] Kloss Yu. Yu., Cheremisin F. G., Khokhlov N. I., Shurygin B. A., “Programmno-modeliruyuschaya sreda dlya issledovaniya techenii gaza v mikro- i nanostrukturakh na osnove resheniya uravneniya Boltsmana”, Atomnaya energiya, 105:4 (2008), 211–213

[12] Titarev V. A., “Neyavnyi chislennyi metod rascheta prostranstvennykh techenii razrezhennogo gaza na nestrukturirovannykh setkakh”, Zh. vychisl. matem. i matem. fiz., 50:10 (2010), 1811–1826 | MR | Zbl

[13] Kolobov V. I., Arslanbekov R. R., Aristov V. V. et al., “Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement”, J. Comput. Phys., 223 (2007), 589–608 | DOI | Zbl

[14] Titarev V. A., Shakhov E. M., “Chislennyi analiz vintovogo dvizheniya Kuetta razrezhennogo gaza mezhdu koaksialnymi tsilindrami”, Zh. vychisl. matem. i matem. fiz., 46:3 (2006), 527–535 | MR | Zbl

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