A numerical method for solving the radiation transport equation in planar and spherical geometry
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 8, pp. 1210-1223 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A computational scheme is proposed for the numerical solution of the stationary radiation transport equation ignoring scattering. It is proved that, at large optical thicknesses, the cosines and absorption coefficients averaged over the one-sided radiation intensities cannot be used in the zeroth approximation and it is necessary to use their first approximation.
@article{ZVMMF_1990_30_8_a8,
     author = {V. I. Gryn' and A. I. Marchenko and V. V. Urban},
     title = {A~numerical method for solving the radiation transport equation in planar and spherical geometry},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1210--1223},
     year = {1990},
     volume = {30},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_8_a8/}
}
TY  - JOUR
AU  - V. I. Gryn'
AU  - A. I. Marchenko
AU  - V. V. Urban
TI  - A numerical method for solving the radiation transport equation in planar and spherical geometry
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1990
SP  - 1210
EP  - 1223
VL  - 30
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_8_a8/
LA  - ru
ID  - ZVMMF_1990_30_8_a8
ER  - 
%0 Journal Article
%A V. I. Gryn'
%A A. I. Marchenko
%A V. V. Urban
%T A numerical method for solving the radiation transport equation in planar and spherical geometry
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1990
%P 1210-1223
%V 30
%N 8
%U http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_8_a8/
%G ru
%F ZVMMF_1990_30_8_a8
V. I. Gryn'; A. I. Marchenko; V. V. Urban. A numerical method for solving the radiation transport equation in planar and spherical geometry. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 8, pp. 1210-1223. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_8_a8/

[1] Chetverushkin B. N., Matematicheskoe modelirovanie zadach dinamiki izluchayuschego gaza, Nauka, M., 1985 | Zbl

[2] Vyskrebentsev A. I., “Metod chislennogo resheniya uravneniya perenosa izlucheniya v odnomernykh zadachakh gazovoi dinamiki”, Zh. vychisl. matem. i matem. fiz., 21:5 (1981), 1206–1214 | MR | Zbl

[3] Gryn V. I., “Skhemy rascheta perenosa izlucheniya”, Dinamika izluchayuschego gaza, VTs AN SSSR, M., 1981, 17–55 | MR

[4] Gryn V. I., Pryamye i obratnye zadachi dinamiki izluchayuschego gaza, Dis. ...dokt. fiz.-matem. nauk, VTs AN SSSR, M., 1988

[5] Golub A. P., “Chislennyi metod resheniya uravnenii perenosa izlucheniya v odnomernykh zadachakh radiatsionnoi gazovoi dinamiki”, Zh. vychisl. matem. i matem. fiz., 23:1 (1983), 142–151 | MR | Zbl

[6] Charakhchyan A. A., “Ob odnoi chislennoi skheme dlya uravneniya perenosa na opticheski gruboi setke”, Zh. vychisl. matem. i matem. fiz., 15:4 (1975), 999–1005 | MR

[7] Goldin V. Ya., Chetverushkin B. N., “Metody resheniya odnomernykh zadach radiatsionnoi gazovoi dinamiki”, Zh. vychisl. matem. i matem. fiz., 12:4 (1972), 990–1000 | MR

[8] Bashurin V. P., Varlamov Yu. V., Goldin V. Ya., Chetverushkin B. N., “Metody resheniya odnomernykh zadach radiatsionnoi gazovoi dinamiki, II”, Zh. vychisl. matem. i matem. fiz., 13:5 (1973), 1298–1306

[9] Germogenova T. A., Sushkevich T. A., “Reshenie uravneniya perenosa metodom srednikh potokov”, Vopr. fiz. zaschity reaktorov, 3, Atomizdat, M., 1969, 34–43 | MR

[10] Nemchinov I. V., “Ob osrednennykh uravneniyakh perenosa izlucheniya i ikh ispolzovanii pri reshenii gazodinamicheskikh zadach”, Prikl. matem. i mekhan., 34:4 (1970), 706–722

[11] Nemchinov I. V., Osrednenie uravnenii perenosa izlucheniya v zadachakh radiatsionnoi gazovoi dinamiki, Dep. v VINITI, No 1721-83 Dep.

[12] Bazylev B. N., Romanov G. S., “Chislennoe reshenie spektralnoi radiatsionno-gazodinamicheskoi zadachi o luchistom okhlazhdenii sfericheskogo ob'ema plazmy s uchetom nestatsionarnosti protsessa perenosa izlucheniya”, Inzh.-fiz. zh., 41:2 (1931), 319–327

[13] Zeldovich Ya. B., Raizer Yu. P., Fizika udarnykh voln i vysokotemperaturnykh gidrodinamicheskikh yavlenii, Nauka, M., 1966

[14] Nemchinov I. V., Trubetskaya I. A., Shuvalov V. V., “Intensivno izluchayuschie sverkhkriticheskie udarnye volny”, Zh. prikl. mekhan. i tekhn. fiz., 1986, no. 2, 112–119

[15] Elyashevich M. A., Romanov G. S., Stankevich Yu. A., “Raschet parametrov svetoerozionnykh plazmennykh fakelov s uchetom spektralnoi zavisimosti ikh izluchatelnykh kharakteristik”, Dinamika izluch. gaza, Tr. IV Vses. konf., v. 1, Izd-vo MGU, M., 1981, 90–101

[16] Romanov G. S., Urban V. V., “Raschet parametrov impulsnogo istochnika sveta na osnove vzryvnogo plazmennogo generatora”, Dinamika izluch. gaza, Tr. IV Vses. konf., v. 1, Izd-vo MGU, M., 1981, 12–20

[17] Degtyarev L. M., Favorskii A. P., “Potokovyi variant metoda progonki”, Zh. vychisl. matem. i matem. fiz., 8:3 (1968), 679–684 | MR

[18] Degtyarev L. M., Favorskii A. P., “Potokovyi variant metoda progonki dlya raznostnykh zadach s silno menyayuschimisya koeffitsientami”, Zh. vychisl. matem. i matem. fiz., 9:1 (1969), 211–218 | MR | Zbl

[19] Gryn V. I., “Ob ustoichivosti matrichnogo varianta potokovoi progonki”, Zh. vychisl. matem. i matem. fiz., 25:3 (1985), 335–343 | MR | Zbl

[20] Romanov G. S., Bazylev B. N., Stepanov K. L., “Luchistoe okhlazhdenie razletayuschegosya v vakuum sfericheskogo oblaka polnostyu ionizovannogo gaza”, Dokl. AN BSSR, 22:2 (1978), 138–141

[21] Rikhtmaier R., Morton K., Raznostnye metody resheniya kraevykh zadach, Mir, M., 1972