Geodesic
A collocation-grid method on moving grids for the numerical modelling of boundary layers
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 4, pp. 521-534 
B. P. Kolobov; J. L. Korobitsina; A. V. Plyasunova; A. G. Sleptsov. A collocation-grid method on moving grids for the numerical modelling of boundary layers. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 4, pp. 521-534. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_4_a4/
@article{ZVMMF_1990_30_4_a4,
     author = {B. P. Kolobov and J. L. Korobitsina and A. V. Plyasunova and A. G. Sleptsov},
     title = {A~collocation-grid method on moving grids for the numerical modelling of boundary layers},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {521--534},
     year = {1990},
     volume = {30},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_4_a4/}
}
TY  - JOUR
AU  - B. P. Kolobov
AU  - J. L. Korobitsina
AU  - A. V. Plyasunova
AU  - A. G. Sleptsov
TI  - A collocation-grid method on moving grids for the numerical modelling of boundary layers
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1990
SP  - 521
EP  - 534
VL  - 30
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_4_a4/
LA  - ru
ID  - ZVMMF_1990_30_4_a4
ER  - 
%0 Journal Article
%A B. P. Kolobov
%A J. L. Korobitsina
%A A. V. Plyasunova
%A A. G. Sleptsov
%T A collocation-grid method on moving grids for the numerical modelling of boundary layers
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1990
%P 521-534
%V 30
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_4_a4/
%G ru
%F ZVMMF_1990_30_4_a4

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

A collocation-grid method of arbitrary order of accuracy is proposed for the numerical solution of systems of equations, including the boundary-layer equations, using grids that adapt to the solution. Results of calculations for laminar and turbulent plane boundary layers without a pressure gradient, as well as turbulent boundary layers with small polymer impurities and laminar boundary layers with a pressure gradient are presented.

[1] Kolobov B. P., Sleptsov A. G., “Novyi metod postroeniya raznostnykh skhem dlya obyknovennykh differentsialnykh uravnenii i ego primenenie k resheniyu zadachi gidrodinamicheskoi ustoichivosti”, Chisl. metody mekhan. sploshnoi sredy, 3, no. 1, VTs SO AN SSSR, Novosibirsk, 1972, 61–77

[2] Russel R. D., Shampine L. F., “A collocation method for boundary value problems”, Numer. Math., 19 (1972), 13–36 | DOI | MR

[3] De Boor C., Swartz B., “Collocation at Gaussian points”, SIAM. J. Numer. Analys., 10 (1973), 582–606 | DOI | MR | Zbl

[4] Plyasunova A. V., Sleptsov A. G., “Kollokatsionno-setochnyi metod resheniya nelineinykh parabolicheskikh uravnenii”, Modelirovanie v mekhan., 1 (18), no. 1, VTs, ITPM SO AN SSSR, Novosibirsk, 1987, 93–108 | MR

[5] Ascher V., Christiansen J., Russel R. D., “Collocation solver for mixed order systems of boundary-value problems”, Math. Comput., 33:146 (1979), 659–679 | DOI | MR | Zbl

[6] Ascher V., Christiansen J., Russel R. D., “Collocation software for boundary-value ODES”, ACM Trans. Math. Software, 7:2 (1981), 209–222 | DOI | MR | Zbl

[7] Kolobov V. D., Novyi psevdogrinovskii variant metodov konechnykh elementov vysokikh poryadkov tochnosti, Preprint No 29–84, ITPM SO AN SSSR, Novosibirsk, 1984

[8] Plyasunova A. V., Sleptsov A. G., “Kollokatsionno-setochnyi metod resheniya nelineinykh parabolicheskikh uravnenii na podvizhnykh setkakh”, Modelirovanie v mekhan., 1 (18), no. 4, VTs, ITPM SO AN SSSR, Novosibirsk, 1987, 116–137 | MR

[9] Plyasunova A. V., “O skhodimosti kollokatsionno-setochnogo metoda dlya lineinykh parabolicheskikh uravnenii”, Modelirovanie v mekhan., 2 (19), no. 1, VTs, ITPM SO AN SSSR, Novosibirsk, 1988, 116–122 | MR

[10] Shlikhting G., Teoriya pogranichnogo sloya, Nauka, M., 1969

[11] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Nauka, M., 1970 | MR

[12] Kolobov B. P., Popkov A. N., “Chislennoe issledovanie turbulentnykh techenii s polimerami v dvumernom pogranichnom sloe”, Chisl. modelirovanie v dinam. zhidkosti, VTs, ITPM SO AN SSSR, Novosibirsk, 1983, 41–50

[13] Babenko K. I., Osnovy chislennogo analiza, Nauka, M., 1986 | MR

[14] Marchuk G. I., Agoshkov V. I., Vvedenie v proektsionno-setochnye metody, Nauka, M., 1981 | MR

[15] Kolobov B. P., Popkov A. N., “Modelirovanie dvumernogo turbulentnogo pogranichnogo sloya”, Chisl. metody v mekhan. zhidkosti i gaza, VTs, ITPM SO AN SSSR, Novosibirsk, 1983, 62–77

[16] Mysovskikh I. P., Interpolyatsionnye kubaturnye formuly, Nauka, M., 1981 | MR | Zbl

[17] Shulman Z. P., Pokryvailo N. A., Kaberdina E. B., “Turbulentnyi massoobmen i diffuziya v polimernykh rastvorakh, snizhayuschikh soprotivlenie treniya”, Inzh.-fiz. zhurnal, 54:6 (1988), 963–970 | MR