Geodesic
About filtration account the crosspiece
Matematičeskoe modelirovanie, Tome 23 (2011) no. 2, pp. 148-158.

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

In clause the new direct hydromechanical decision of one of difficult of tasks of the theory of a filtration – task free of a filtration through the crosspiece based on use of a method consecutive (17-th) conformation of displays for translation of area of a filtration on area godogrofa of speed of a filtration is given. The received settlement dependences expressed in elementary functions, allow in an obvious kind to define meanings of speeds of a filtration and directions of a line of currents in any point of area of a filtration for the crosspieces with the given boundary conditions. The results of calculations on them practically completely coincide with the known data of the exact and numerical decisions for special cases. A picture of a field of complete speeds of a filtration as family of izot-lines of equal speeds for the first time is given, are constructed diagrams of speeds of a filtration on the arbitrary chosen lines. The decision allowing practically exact to express modulation elliptic function through is received also elementary.
Keywords: without pressure head a filtration, a crosspiece, consecutive conforming displays, a current line, hodograph speeds of a filtration, modulating function. 
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K. N. Anakhayev. About filtration account the crosspiece. Matematičeskoe modelirovanie, Tome 23 (2011) no. 2, pp. 148-158. http://geodesic.mathdoc.fr/item/MM_2011_23_2_a10/

[1] Hamel G., “Uber Grundwasserstromung”, Zeitschrift fur angewante Mathematik und Mechanik, 14:3 (1934), 129–159 | DOI

[2] Hamel G., Gunther E., “Numerische Durchrechnung zu der Abhandlung uber Grundwasserstromung”, Zeitschrift fur angewante Mathematik und Mechanik, 15:3 (1935), 255–265 | DOI | Zbl

[3] Muskat M., “Seepage of water through dams with vertical Faces”, Journal of General and Applied Physics, 6 (1935), 402–415 | Zbl

[4] Masket M., Techenie odnorodnykh zhidkostei v poristoi srede, per. s angl., M., 1949, 628 pp. | Zbl

[5] Charnyi I. A., “Strogoe dokazatelstvo formul Dyupyui dlya beznapornoi filtratsii s promezhutkom vysachivaniya”, DAN SSSR, 79:6 (1951), 937–940

[6] Polubarinova-Kochina P. Ya., Nekotorye zadachi ploskogo dvizheniya gruntovykh vod, Institut mekhaniki AN SSSR, M.–L., 1942, 143 pp.

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

[8] I. M. Vinogradov (gl. red.), Matematicheskaya entsiklopediya, v. 3, KOO-OD, Sov. entsiklopediya, M., 1982, 1183 pp. | MR

[9] Hornung U., Krueger T., “Evaluation of the Polubarinova-Kochina Formula for the Dam problem”, Water Resources Researth, 21:3 (1985), 395–398 | DOI

[10] Khairullin Z. E., “Issledovanie vliyaniya neodnorodnosti yadra kamenno-zemlyanoi plotiny na filtratsionnye kharakteristiki”, Trudy seminara po kraevym zadacham, 19, Izd-vo Kazanskogo univer-ta, Kazan, 1983, 202–210 | Zbl

[11] Bereslavskii E. N., Numerov S. P., Panasenko L. A., “O primenenii metoda granichnykh integralnykh uravnenii k resheniyu nekotorykh zadach filtratsii”, Izv. VNIIG, 151 (1981), 3–7

[12] Proskurnikov S., “Novye raschetnye dannye po filtratsii cherez zemlyanye peremychki”, Trudy GGI, 1937, no. 5, 162–182

[13] Anakhaev K. N., “Raschet filtratsii cherez gruntovuyu peremychku na nepronitsaemom osnovanii”, Izv. vuzov. Stroitelstvo i arkhitektura, 1990, no. 7, 78–82

[14] Anakhaev K. N., Sovershenstvovanie konstruktsii, metodov raschetnogo obosnovaniya i proektirovaniya protivofiltratsionnykh ustroistv gruntovykh plotin, Dis. d-ra tekhn. nauk (05.23.07), MGUP, M., 1997, 521 pp.