Geodesic
Modeling of the base of a~hydraulic structure with constant flow velocity sections and a~curvilinear confining layer
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2009), pp. 73-79.

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

We construct the underground contour of a rectangular subsurface dam, whose corners are rounded in accordance with curves of constant filtration velocity and whose water-permeable base is underlain by a curvilinear confining layer. The latter is assumed to have a horizontal part, while the rest sections are assumed to have a constant flow velocity. We obtain an analytic solution of the corresponding mixed problem of the theory of analytic functions. We adduce results of numerical tests and consider the limit case studied earlier by P. Ya. Polubarinova-Kochina and I. N. Kochina.
Mots-clés : filtration, dam
Keywords: groundwater, velocity hodograph, conformal mappings. 
@article{IVM_2009_3_a4,
     author = {\`E. N. Bereslavskii and L. A. Aleksandrova},
     title = {Modeling of the base of a~hydraulic structure with constant flow velocity sections and a~curvilinear confining layer},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {73--79},
     publisher = {mathdoc},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_3_a4/}
}
TY  - JOUR
AU  - È. N. Bereslavskii
AU  - L. A. Aleksandrova
TI  - Modeling of the base of a~hydraulic structure with constant flow velocity sections and a~curvilinear confining layer
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2009
SP  - 73
EP  - 79
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2009_3_a4/
LA  - ru
ID  - IVM_2009_3_a4
ER  - 
%0 Journal Article
%A È. N. Bereslavskii
%A L. A. Aleksandrova
%T Modeling of the base of a~hydraulic structure with constant flow velocity sections and a~curvilinear confining layer
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2009
%P 73-79
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2009_3_a4/
%G ru
%F IVM_2009_3_a4
È. N. Bereslavskii; L. A. Aleksandrova. Modeling of the base of a~hydraulic structure with constant flow velocity sections and a~curvilinear confining layer. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2009), pp. 73-79. http://geodesic.mathdoc.fr/item/IVM_2009_3_a4/

[1] Kochina I. N., Polubarinova-Kochina P. Ya., “O primenenii plavnykh konturov osnovaniya gidrotekhnicheskikh sooruzhenii”, PMM, 16:1 (1952), 55–66

[2] Polubarinova-Kochina P. Ya., Teoriya dvizheniya gruntovykh vod, Gostekhizdat, M., 1977, 664 pp. | MR

[3] Tumashev G. G., Nuzhin M. T., Obratnye kraevye zadachi i ikh prilozheniya, Izd-vo Kazansk. un-ta, Kazan, 1965, 333 pp. | MR

[4] Aksentev L. A., Ilinskii N. B., Nuzhin M. T., Salimov R. B., Tumashev G. G., “Teoriya obratnykh kraevykh zadach dlya analiticheskikh funktsii i ee prilozheniya”, Itogi nauki i tekhniki. Ser. Matem. analiz, 18, VINITI, M., 1980, 67–124 | MR | Zbl

[5] Koppenfels V., Shtalman F., Praktika konformnykh otobrazhenii, In. lit., M., 1963, 406 pp. | Zbl

[6] Aravin V. I., Numerov S. N., Teoriya dvizheniya zhidkostei i gazov v nedeformiruemoi poristoi srede, Gostekhizdat, M., 1959, 616 pp.

[7] Bereslavskii E. N., “O differentsialnykh uravneniyakh klassa Fuksa, svyazannykh s konformnym otobrazheniem krugovykh mnogougolnikov v polyarnykh setkakh”, Differents. uravneniya, 33:3 (1997), 296–301 | MR | Zbl

[8] Bereslavskii E. N., “O konformnom otobrazhenii nekotorykh krugovykh mnogougolnikov na pryamougolnik”, Izv. vuzov. Matematika, 1980, no. 5, 3–7 | MR | Zbl

[9] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Nauka, M., 1971, 1108 pp.

[10] Bereslavskii E. N., “Opredelenie podzemnogo kontura zaglublennogo flyubeta s uchastkom postoyannoi skorosti pri nalichii solenykh podpornykh vod”, PMM, 62:1 (1988), 169–175 | MR