Geodesic
An efficient numerical algorithm for simulating a two-dimensional glow discharge
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 11, pp. 2065-2080
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A numerical algorithm of the second approximation order with respect to the space variables for simulating a two-dimensional elevated pressure glow discharge in the framework of the drift-diffusion approximation is presented. A specific feature of this algorithm is the use of the Laplace resolving operator for the solution of the system of grid equations. This makes it possible to ensure the convergence of the solution in strong grid norms. Mathematical aspects of the statement of the differential-difference and finite difference problems (solvability, nonnegativity, approximation, stability, and convergence) are discussed, and bounds on the norms of the corresponding differential and difference operators that are required for constructing an optimal iterative process are obtained. 
@article{ZVMMF_2006_46_11_a11,
     author = {R. Sh. Islamov},
     title = {An efficient numerical algorithm for simulating a~two-dimensional glow discharge},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2065--2080},
     year = {2006},
     volume = {46},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a11/}
}
TY  - JOUR
AU  - R. Sh. Islamov
TI  - An efficient numerical algorithm for simulating a two-dimensional glow discharge
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 2065
EP  - 2080
VL  - 46
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a11/
LA  - ru
ID  - ZVMMF_2006_46_11_a11
ER  - 
%0 Journal Article
%A R. Sh. Islamov
%T An efficient numerical algorithm for simulating a two-dimensional glow discharge
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 2065-2080
%V 46
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a11/
%G ru
%F ZVMMF_2006_46_11_a11
R. Sh. Islamov. An efficient numerical algorithm for simulating a two-dimensional glow discharge. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 11, pp. 2065-2080. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a11/

[1] Gladush G. G., Samokhin A. A., “Vliyanie nachalnoi kontsentratsii plazmy na dlitelnost odnorodnogo goreniya tleyuschego razryada”, Fiz. plazmy, 11:2 (1985), 230–235

[2] Raizer Yu. P., Surzhikov S. T., “Dvumernaya struktura normalnogo tleyuschego razryada i rol diffuzii v formirovanii katodnogo i anodnogo tokovykh pyaten”, Teplofiz. vysokikh t-r, 26:3 (1988), 428–435

[3] Islamov R. Sh., “Chislennoe issledovanie perekhodnykh form razryada ot temnogo taundsendovskogo k anomalnomu tleyuschemu”, Izv. RAN. Ser. fiz., 64:7 (2000), 1407–1410

[4] Islamov R. Sh., “Globalnye resheniya uravnenii diffuzionno-dreifovogo priblizheniya v teorii gazovogo razryada”, Differents. ur-niya, 39:12 (2003), 1662–1676 | MR | Zbl

[5] Islamov R. Sh., “O regulyarnosti resheniya uravnenii diffuzionno-dreifovogo priblizheniya v teorii gazovogo razryada”, Zh. vychisl. matem. i matem. fiz., 46:1 (2006), 131–147 | MR | Zbl

[6] Islamov R. Sh., Gulamov E. N., “Numerical simulation of axisymmetric anode spot formation in glow discharge at elevated pressure”, IEEE Trans. Plasma Sci., 26:1 (1998), 7–13 | DOI

[7] Islamov R. Sh., “Modelirovanie samoorganizatsii tokovykh struktur v tleyuschem razryade”, Izv. RAN. Ser. fiz., 64:7 (2000), 1402–1406

[8] Islamov R. Sh., Novodvorskii O. A., Sagdeev R. Ya., “Tokovye polosy na poverkhnosti anoda v tleyuschem razryade v potoke i effekt udvoeniya ikh prostranstvennogo perioda”, Fiz. plazmy, 23:10 (1997), 970–976

[9] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1977 | MR | Zbl

[10] Samarskii A. A., Gulin A. B., Ustoichivost raznostnykh skhem, Nauka, M., 1973 | Zbl

[11] Samarskii A. A., Vabischevich P. N., Chislennye metody resheniya zadach konvektsii-diffuzii, Editorial URSS, M., 1999

[12] Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR

[13] Gilbarg D., Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | MR | Zbl

[14] Khokni R., “Metody rascheta potentsiala i ikh prilozheniya”, Vychisl. metody v fiz. plazmy, eds. B. Older, S. Fernbakh, M. Rotenberg, Mir, M., 1974

[15] Ilin V. P., Chislennye metody resheniya zadach elektrofiziki, Nauka, M., 1985 | MR

[16] Islamov R. Sh., “Samoorganizatsiya tokovykh struktur v gazovom razryade”, Sovremennye lazerno-informatsionnye i lazernye tekhnologii, eds. V. Ya. Panchenko, B. C. Golubev, Interkontakt Nauka, M., 2005, 260–274 http://www.laser.ru/science/pdf/select42.pdf