Flows in channel under evaporation from the free surface groundwater and the capillary ground

E. N. Bereslavskii ; N. V. Zakharenkova

Matematičeskoe modelirovanie, Tome 22 (2010) no. 7, pp. 22-32.

Résumé

In two-dimensional steady filtration are considered some of the mathematical models of groundwater flow from the channel in the presence of evaporation from the free surface. For their study and formulated using the method Polubarinova-Kochina solve mixed boundary value problems of the theory of analytic functions. On the basis of these models are developed algorithms for calculating the size of the saturated zone in situations where the filtration is taken into account capillarity of soil or water level in the channel. Using exact analytical dependences obtained and numerical calculations carried out a detailed analysis of the structure and characteristics of the simulated processes, as well as the influence of all the physical characteristics of the models on the size of the zone of saturation.

Détail

Mots-clés : filtration, canal
Keywords: ground water, evaporation, capillarity of the soil, the complex flow velocity, the method Polubarinova-Kochina, linear differential equations of the Fuchs class, conformal mapping.

Bibliographie

[1] Vedernikov V. V., “Vliyanie kapillyarnogo podnyatiya na filtratsiyu iz kanalov”, Gidrotekhn. str-vo, 1935, no. 3, 20–27 | MR

[2] Vedernikov V. V., “Vliyanie kapillyarnosti grunta na filtratsiyu so svobodnoi poverkhnosti”, Dokl. AN SSSR, 3:4 (1936), 157–161

[3] Vedernikov V. V., Teoriya filtratsii i ee primenenie v oblasti irrigatsii i drenazha, Gosstroiizdat, M.–L., 1938, 248 pp.

[4] Vedernikov V. V., “Uchet vliyaniya kapillyarnosti grunta na filtratsiyu iz kanalov”, Dokl. AN SSSR, 28:5 (1940), 408–410

[5] Rizenkampf B. K., “Gidravlika gruntovykh vod, 3”, Uch. zapiski Saratovsk. un-ta. Ser. gidravliki, 15:5 (1940), 3–93 | MR

[6] Verigin N. N., “Filtratsiya vody iz orositelya irrigatsionnoi sistemy”, Dokl. AN SSSR, 66:4 (1949), 589–592 | MR

[7] Verigin N. N., “Nekotorye sluchai pod'ema gruntovykh vod pri obschei i mestnoi usilennoi infiltratsii”, Inzh. sb., 7 (1950), 21–34

[8] Aravin V. I., Numerov S. N., Teoriya dvizheniya zhidkostei i gazov v nedeformiruemoi poristoi srede, Gostekhizdat, M., 1953, 616 pp.

[9] Numerov S. N., “Ob odnom sposobe resheniya filtratsionnykh zadach”, Izv. AN SSSR. OTN, 1954, no. 4, 133–139 | MR

[10] Bereslavskii E. N., “K zadache o filtratsii iz orositelya irrigatsionnoi sistemy”, Izv. AN SSSR. MZhG, 1987, no. 2, 105–109

[11] Kasimov A. R., “Filtratsionnaya optimizatsiya formy zemlyanogo kanala s uchetom kapillyarnosti”, Vychisl. i prikl. matem., 61, Izd-vo Kievsk. un-ta, Kiev, 1987, 70–74

[12] Kasimov A. R., “Filtratsionnyi raschet drenazha metodom obratnykh kraevykh zadach”, Tr. sem. po kraevym zadacham, 23, Izd-vo Kazan. un-ta, Kazan, 1987, 94–102

[13] Bereslavskii E. N., Matveev V. V., “Filtratsiya iz kanalov maloi glubiny i orositelei”, Izv. AN SSSR. MZhG, 1989, no. 1, 96–102

[14] Bereslavskii E. N., “O rezhime gruntovykh vod pri filtratsii iz orositelya irratsionnoi sistemy”, PMTF, 1989, no. 5, 88–91

[15] Bereslavskii E. N., Matveev V. V., “Filtratsiya v pochvogruntakh, podstilaemykh silnopronitsaemym napornym gorizontom”, Izv. AN SSSR. MZhG, 1991, no. 2, 95–104

[16] Golubev V. V., Lektsii po analiticheskoi teorii differentsialnykh uravnenii, Gostekhizdat, M.–L., 1950, 436 pp.

[17] Polubarinova-Kochina P. Ya., Teoriya dvizheniya gruntovykh vod, 2-e izd., Gostekhizdat, M., 1952, 676 pp. | MR

[18] Mikhailov G. K., Nikolaevskii V. N., “Dvizhenie zhidkostei i gazov v poristykh sredakh”, Mekhanika v SSSR za 50 let, v. 2, Nauka, M., 1970, 585–648

[19] Kochina P. Ya., Bereslavskii E. N., Kochina N. N., Analiticheskaya teoriya lineinykh differentsialnykh uravnenii klassa Fuksa i nekotorye zadachi podzemnoi gidromekhaniki, 1, preprint No 576, In-t problem mekhaniki RAN, M., 1996, 122 pp.

[20] Bereslavskii E. N., “Ob integrirovanii v zamknutoi forme nekotorykh differentsialnykh uravnenii klassa Fuksa, vstrechayuschikhsya v gidro- i aeromekhanike”, Dokl. RAN, 428:4 (2009), 439–443 | MR | Zbl

[21] 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

[22] Bereslavskii E. N., Panasenko L. A., “Ob opredelenii razmerov zony nasyscheniya pri filtratsii iz kanala s maloi glubinoi vody”, PMTF, 1981, no. 5, 92–94 | MR