Modeling the Movement of Groundwater from the Pits, Surrounded with Tongues of Zhukovsky

Bereslavckii Eduard Naumovich

doi:doi:10.11648/j.ijtam.20170304.11

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Modeling the Movement of Groundwater from the Pits, Surrounded with Tongues of Zhukovsky

Bereslavckii Eduard Naumovich

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 4)

Received: 8 May 2017 Accepted: 1 June 2017 Published: 21 July 2017

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Abstract

In the hydrodynamic statement the filtration low from ditches, walled tongues of Zhukovsky is considered. The fluid moves through the layer of soil, underlain by a well-permeable pressure aquifer, which is contained waterproof area on the roof. For study the infiltration to the free surface of groundwater is formulated a mixed multi-parameter boundary value problem of the theory of analytic function, which is solved by the Polubarinova-Kochina's method and ways the conformal mapping areas of a special kind, which are characteristic for tasks of an underground hydromechanics.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 4)
DOI	10.11648/j.ijtam.20170304.11
Page(s)	129-137
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Filtration, Infiltration, Groundwater Aquifers, Ditch, Tongue of Zhukovsky, Polubarinova-Kochina's Method, Fuchs Differential Equations, Complex Flow Velocity, Conformal Mappings

References

[1]	V. V. Vedernikov. Influence of capillary rise in the filtration channel // Hydraulic engineering. 1935. №5. P. 20-27.
[2]	V. V. Vedernikov. Influence of soil capillary seepage with free surface // Dokl. USSR Academy of Sciences. 1936. T. III (12). № 4 (99). P.157-161.
[3]	V. I. Aravin. The inflow of groundwater to the trenches, fences tongue // Math. VNIIG. 1937. T. 20. S.74-89.
[4]	V. S. Kozlov. Hydromechanical calculation sheet jumpers // Math. USSR Academy of Sciences. OTN. 1939. №6. P.89-110.
[5]	V. V. Vedernikov. Filtration Theory and its application in the field of irrigation and drainage. M.; L.: Gosstroiizdat. 1939. 248 p.
[6]	F. B. Nelson-Skornyakov. Hydro water flow calculation to the trench // Math. USSR Academy of Sciences. OTN. 1943. №7. P. 90-94.
[7]	F. B. Nelson-Skornyakov. Some cases pritekaniya ground water from the river to the career (trench) // Math. USSR Academy of Sciences. OTN. 1944. №3. S.209-220.
[8]	F. B. Nelson-Skornyakov. Filtration in a homogeneous medium. M.: Soviet science. 1947. 279 p.; 2nd ed. 1949. 568 p.
[9]	V. I. Aravin and S. N. Numerov. Filtration calculations of hydraulic structures. M.: Stroyizdat. 1948. 227 p.
[10]	V. V. Vedernikov. Filtering in the presence of drainage or aquifer // Dokl. USSR Academy of Sciences. 1949. T.69. №5. S.619-622.
[11]	L. D Aptekar. Questions filtration calculation of horizontal drainage shipping locks and dry docks // Izv. VNIIG. 1951. T.46. S.80-105.
[12]	P. Y. Polubarinova-Kochina Theory of movement of groundwater. M.: Gostekhizdat. 1952. 676 p.; 2nd ed. M.: Nauka. 1977. 664 p.
[13]	V. I. Aravin and S. N. Numerov. Theory fluids movement deformable porous media. M.: Gostekhizdat. 1953. 616 p.
[14]	Development of filtration theory research in the USSR (1917-1967). M.: Nauka. 1969. 545 p.
[15]	G. K. Mikhailov, V. N. Nicholaevskii. The movement of fluids in porous media // Mechanics in the USSR for 50 years. M.: Nauka. 1970. Vol. 2. S. 585-648.
[16]	P. Y. Polubarinova-Kochina. Selected tr. The hydrodynamics and the theory of filtration. M.: Nauka. 1991. 351 p.
[17]	N. E. Zhukovsky. Seepage of water through the dam // Coll. Vol. M.: Gostekhizdat. 1950. T.7. S.297-332.
[18]	E. N. Bereslavskii. Some hydrodynamic models related to the problem of the flow of Zhukovsky tongue // Dokl. Russian Academy of Sciences. 2013. T.448. Number 5. S.529-533.
[19]	E. N. Bereslavskii. On some mathematical models related to the problem of the flow of Zhukovsky tongue // J. Appl. Math. and Mech. 2014. T.78. Vol.3. Pp 394-410.
[20]	E. N. Bereslavskii, P. Y. Polubarinova-Kochina. On some classes of equations of Fuchs in hydro and Aeromechanics // Math. Russian Academy of Sciences. Fluid Dynamics. 1992. №5. P.3-7.
[21]	E. N. Bereslavskii, P. Y. Polubarinova-Kochina. Differential equations of Fuchs class encountered some problems of mechanics of liquids and gases // Math. Russian Academy of Sciences. Fluid Dynamics. 1997. № 5. P. 9-17.
[22]	E. N. Bereslavskii. Conformal mapping of some circular polygons on a rectangle // Izv. Vuzov. Mathematics. 1980. №5. P.3-7.
[23]	E. N. Bereslavskii. Differential equations of Fuchs class associated with the conformal mapping of circular polygons in polar grids // Differents. equation. 1997. T.33. No. 3. P.296-301.
[24]	E. N. Bereslavskii. On some differential equations class Fuchs, occurring in problems of mechanics of liquids and gases // Differents. equation. 2012. T.48. №4. P.590-594.
[25]	E. N. Bereslavskii. Application of Polubarinova-Kochina to study seepage flows from the trenches, fenced tongue Zhukovsky // Dokl. RAN.2014. T.455. Number 6. P. 651-655.
[26]	Koppenfels W, Stallmann F. Praxis der Konformen Abbildung. Berlin: Springer, 1959 = Koppenfels V., F. Shtalman practice of conformal mappings. M.: IL. 1963.406 p.
[27]	V. V. Golubev. Lectures on the analytic theory of differential equations. M.; L.: Gostekhizdat. 1950. 436 p.
[28]	I. S. Gradshtein, I. M. Ryzhik. Tables of integrals, sums, series and products. M.: Nauka. 1971. 1108 p.
[29]	E. N. Bereslavskii. Simulation flow tongue Zhukovsky // Reports of the Russian Academy of Sciences. 2011. T.440. №1. S.47-51.
[30]	E. N. Bereslavskii. About groundwater flow regime at the tongue Zhukovsky // J. Appl.Math. and Mech. 2011. T.75. Vol. 2. P.303-313.

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Bereslavckii Eduard Naumovich. (2017). Modeling the Movement of Groundwater from the Pits, Surrounded with Tongues of Zhukovsky. International Journal of Theoretical and Applied Mathematics, 3(4), 129-137. https://doi.org/10.11648/j.ijtam.20170304.11

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ACS Style

Bereslavckii Eduard Naumovich. Modeling the Movement of Groundwater from the Pits, Surrounded with Tongues of Zhukovsky. Int. J. Theor. Appl. Math. 2017, 3(4), 129-137. doi: 10.11648/j.ijtam.20170304.11

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AMA Style

Bereslavckii Eduard Naumovich. Modeling the Movement of Groundwater from the Pits, Surrounded with Tongues of Zhukovsky. Int J Theor Appl Math. 2017;3(4):129-137. doi: 10.11648/j.ijtam.20170304.11

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@article{10.11648/j.ijtam.20170304.11,
  author = {Bereslavckii Eduard Naumovich},
  title = {Modeling the Movement of Groundwater from the Pits, Surrounded with Tongues of Zhukovsky},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {4},
  pages = {129-137},
  doi = {10.11648/j.ijtam.20170304.11},
  url = {https://doi.org/10.11648/j.ijtam.20170304.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170304.11},
  abstract = {In the hydrodynamic statement the filtration low from ditches, walled tongues of Zhukovsky is considered. The fluid moves through the layer of soil, underlain by a well-permeable pressure aquifer, which is contained waterproof area on the roof. For study the infiltration to the free surface of groundwater is formulated a mixed multi-parameter boundary value problem of the theory of analytic function, which is solved by the Polubarinova-Kochina's method and ways the conformal mapping areas of a special kind, which are characteristic for tasks of an underground hydromechanics.},
 year = {2017}
}

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TY  - JOUR
T1  - Modeling the Movement of Groundwater from the Pits, Surrounded with Tongues of Zhukovsky
AU  - Bereslavckii Eduard Naumovich
Y1  - 2017/07/21
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170304.11
DO  - 10.11648/j.ijtam.20170304.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 129
EP  - 137
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170304.11
AB  - In the hydrodynamic statement the filtration low from ditches, walled tongues of Zhukovsky is considered. The fluid moves through the layer of soil, underlain by a well-permeable pressure aquifer, which is contained waterproof area on the roof. For study the infiltration to the free surface of groundwater is formulated a mixed multi-parameter boundary value problem of the theory of analytic function, which is solved by the Polubarinova-Kochina's method and ways the conformal mapping areas of a special kind, which are characteristic for tasks of an underground hydromechanics.
VL  - 3
IS  - 4
ER  -

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Author Information

Bereslavckii Eduard Naumovich

Department of Applied Mathematics and Informatics, University of Civil Aviation, St. Petersburg, Russia

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APA Style

Bereslavckii Eduard Naumovich. (2017). Modeling the Movement of Groundwater from the Pits, Surrounded with Tongues of Zhukovsky. International Journal of Theoretical and Applied Mathematics, 3(4), 129-137. https://doi.org/10.11648/j.ijtam.20170304.11

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ACS Style

Bereslavckii Eduard Naumovich. Modeling the Movement of Groundwater from the Pits, Surrounded with Tongues of Zhukovsky. Int. J. Theor. Appl. Math. 2017, 3(4), 129-137. doi: 10.11648/j.ijtam.20170304.11

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AMA Style

Bereslavckii Eduard Naumovich. Modeling the Movement of Groundwater from the Pits, Surrounded with Tongues of Zhukovsky. Int J Theor Appl Math. 2017;3(4):129-137. doi: 10.11648/j.ijtam.20170304.11

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@article{10.11648/j.ijtam.20170304.11,
  author = {Bereslavckii Eduard Naumovich},
  title = {Modeling the Movement of Groundwater from the Pits, Surrounded with Tongues of Zhukovsky},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {4},
  pages = {129-137},
  doi = {10.11648/j.ijtam.20170304.11},
  url = {https://doi.org/10.11648/j.ijtam.20170304.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170304.11},
  abstract = {In the hydrodynamic statement the filtration low from ditches, walled tongues of Zhukovsky is considered. The fluid moves through the layer of soil, underlain by a well-permeable pressure aquifer, which is contained waterproof area on the roof. For study the infiltration to the free surface of groundwater is formulated a mixed multi-parameter boundary value problem of the theory of analytic function, which is solved by the Polubarinova-Kochina's method and ways the conformal mapping areas of a special kind, which are characteristic for tasks of an underground hydromechanics.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Modeling the Movement of Groundwater from the Pits, Surrounded with Tongues of Zhukovsky
AU  - Bereslavckii Eduard Naumovich
Y1  - 2017/07/21
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170304.11
DO  - 10.11648/j.ijtam.20170304.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 129
EP  - 137
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170304.11
AB  - In the hydrodynamic statement the filtration low from ditches, walled tongues of Zhukovsky is considered. The fluid moves through the layer of soil, underlain by a well-permeable pressure aquifer, which is contained waterproof area on the roof. For study the infiltration to the free surface of groundwater is formulated a mixed multi-parameter boundary value problem of the theory of analytic function, which is solved by the Polubarinova-Kochina's method and ways the conformal mapping areas of a special kind, which are characteristic for tasks of an underground hydromechanics.
VL  - 3
IS  - 4
ER  -

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