Geodesic
Solution method of three-dimentional nonlinear flow equation in confined aquifer with partially penetrating wells
Matematičeskoe modelirovanie, Tome 16 (2004) no. 3, pp. 33-42 
P. A. Mazurov; A. V. Tsepaev. Solution method of three-dimentional nonlinear flow equation in confined aquifer with partially penetrating wells. Matematičeskoe modelirovanie, Tome 16 (2004) no. 3, pp. 33-42. http://geodesic.mathdoc.fr/item/MM_2004_16_3_a3/
@article{MM_2004_16_3_a3,
     author = {P. A. Mazurov and A. V. Tsepaev},
     title = {Solution method of three-dimentional nonlinear flow equation in confined aquifer with partially penetrating wells},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {33--42},
     year = {2004},
     volume = {16},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_3_a3/}
}
TY  - JOUR
AU  - P. A. Mazurov
AU  - A. V. Tsepaev
TI  - Solution method of three-dimentional nonlinear flow equation in confined aquifer with partially penetrating wells
JO  - Matematičeskoe modelirovanie
PY  - 2004
SP  - 33
EP  - 42
VL  - 16
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MM_2004_16_3_a3/
LA  - ru
ID  - MM_2004_16_3_a3
ER  - 
%0 Journal Article
%A P. A. Mazurov
%A A. V. Tsepaev
%T Solution method of three-dimentional nonlinear flow equation in confined aquifer with partially penetrating wells
%J Matematičeskoe modelirovanie
%D 2004
%P 33-42
%V 16
%N 3
%U http://geodesic.mathdoc.fr/item/MM_2004_16_3_a3/
%G ru
%F MM_2004_16_3_a3

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

A new algorithm of solving flow equation in confined aquifer with large number of wells has been proposed. The non-Darcian law is takes under the rapid rate near the wells. The algorithm is based on the methods the division of domain on subdomains.

[1] Basniev K. S, Vlasov A. M., Kochina I. M., Maksimov V. M., Podzemnaya gidravlika, Nedra, M., 1986, 303 pp.

[2] Roger Beckie, Eric F. Wood, Alvaro A. Aldama, “Mixed Finite Element Simulation of Saturated Groundwater Flow Using a Multigrid Accelerated Domain Decomposition Technique”, Water Resour. Res., 26:9 (1993), 3145–3157

[3] Gander M. J., Golub G. H., “A Non-overlapping optimizid Schwarz method which converges with arbitarily weak dependence on $h$”, Fourteenth International Symposiums on Domain Decomposition Methods for Partial Differential Equqtions, eds. Ismael Herrera, David E. Keyes, Olof B. Widlund, Robert Yates, 2002, 281–288 | MR

[4] Feng X., “A Non-overlapping Domain Decomposition Method for Solving Elliptic Problems by Finite Element Method”, Ninth International Symposiums on Domain Decomposition Methods for Partial Differential Equqtions, eds. Petter E. Bjorstad, Magne S. Espedal, David E. Keyes, 1996, 222–229

[5] Marchuk G. E., Metody vychislitelnoi matematiki, Nauka, M., 1989, 121 pp. | MR

[6] Gai Z, Parashkevov R. R., Russel T. F., Ye X., “Overlapping Domain Decomposition for a Mixed Finite Element Method in Three Dimentions”, Ninth International Symposiums on Domain Decomposition Methods for Partial Differential Equations, eds. Petter E. Bjorstad, Magne S. Espedal, David E. Keyes, 1996, 188–196

[7] Gastaldi F., Gastaldi L. and Quarteroni A., “ADN and ARN Domain Decomposition Methods Advection-Diffusion Equations”, Ninth International Symposiums on Domain Decomposition Methods for Partial Differential Equations, eds. Petter E. Bjorstad, Magne S. Espedal, David E. Keyes, 1996, 334–341

[8] Mazurov P. A., Tsepaev A. V., “K resheniyu zadach filtratsii neszhimaemoi zhidkosti v trekhmernykh plastakh s gidrodinamicheski nesovershennymi skvazhinami”, Mat. modelir., 14:9 (2002), 121–123 | Zbl

[9] Mazurov P. A., Tsepaev A. V., “Metod superpozitsii dlya reshenii zadach filtratsii zhidkosti v trekhmernykh plastakh s gidrodinamicheski nesovershennymi skvazhinami”, Sovremennye problemy gidrogeologii i gidrogeomekhaniki, Izd-vo SpbGU, SPb, 2002, 471–476

[10] Zenkevich O., Morgan K., Konechnye elementy i approksimatsiya, Mir, M., 1986, 318 pp. | MR

[11] Hill M. C., “Solving Groundwater Flow Problems by Conjugate-Gradient Methods and the Strongly Implicit Procedure”, Water Resour. Res., 26:9 (1990), 1961–1969 | DOI

[12] Larabi A., De Smedt F., “Solving three-dimensional hexahedral finite element groundwater models by preconditioned conjugate gradient methods”, Water Resour. Res., 30:2 (1994), 509–521 | DOI