Díaz Díaz, Jesús Ildefonso and Antontsev, S.N. (2008) On the Coupling Between Channel Level and Surface Ground-Water Flows. Pure and Applied Geophysics, 165 (8). pp. 1511-1530. ISSN 0033-4553
Restricted to Repository staff only until 31 December 2020.
This paper is devoted to a mathematical analysis of some general models of mass transport and other coupled physical processes developed in simultaneous flows of surface, soil and ground waters. Such models are widely used for forecasting (numerical simulation) of a hydrological cycle for concrete territories. The mathematical models that proved a more realistic approach are obtained by combining several mathematical models for local processes. The water-exchange models take into account the following factors: Water flows in confined and unconfined aquifers, vertical moisture migration allowing earth surface evaporation, open-channel flow simulated by one-dimensional hydraulic equations, transport of contamination, etc. These models may have different levels of sophistication. We illustrate the type of mathematical singularities which may appear by considering a simple model on the coupling of a surface flow of surface and ground waters with the flow of a line channel or river.
|Uncontrolled Keywords:||Mathematical models; coupled processes; channel and ground waters|
|Subjects:||Sciences > Physics > Geophysics|
ABBOTT, M., BATHURST, J., and CUNGE J. A. (1986), An introduction to the European hydrological system (SHE), Part 2, J. Hydrol. 87, 129–148.
ANTONTSEV, S. N. and DÍAZ, J. I. (1991), Space and time localization in the flow of two immiscible fluids through a porous medium: Energy methods applied to systems, Nonlinear Anal. 16, 299–313.
ANTONTSEV, S. N., DÍAZ, J. I., and SHMAREV, S., Energy Methods for Free Boundary Problems: Applications to Non-linear PDEs and Fluid Mechanics, (Bikha¨user, Boston, 2002) Progress in Nonlinear Differential Equations and their Applications, vol. 48.
ANTONTSEV, S. N., EPIKHOV, G. P., and KASHEVAROV A. A. (1986), Mathematical system modelling of water xchange processes (Nauka, Sibirsk. Otdel., Novosibirsk in Russian).
ANTONTSEV, S. N. and KASHEVAROV, A. A.,. Finite Rate of Propagation of Perturbations in Simultaneous Flows of Surface and Ground Water, (Dinamika Sploshnoi Sredy 57 Institute of Hydrodynamics, Novosibirsk. 1982) pp. 21–27.
ANTONTSEV, S. N. and KASHEVAROV, A. A. (1986), Splitting according to physical processes in the problem of interaction between surface and underground water, Dokl. Akad. Nauk SSSR, 288, pp. 86–90 (English translation: Soviet Phys. Dokl, v. 31, n. 5, pp.381–383).
ANTONTSEV, S. N. and KASHEVAROV, A. A. Localization of solutions of nonlinear parabolic equations that are degenerate on a surface (Dinamika Sploshnoi Sredy 111, Institute of Hydrodynamics, Novosibirsk 1996) pp. 7–14.
ANTONTSEV, S. N. and KASHEVAROV, A. A., Correctness of a hydraulic model of filtration for ground waters with an unsaturated zone. In book Mathematical Models in Filtration and its Applications, (Institute of Hydrodynamics, Novosibirsk, 1999a) pp. 21–35.
ANTONTSEV, S. N. and KASHEVAROV, A. A. (1999b), Mathematical models of mass transfer in interconnected processes of surface, soil and ground waters. Abstracts of the International Conference Modern Approaches to Flows in Porous Media, September 6–8, Moscow, pp. 165–166.
ANTONTSEV, S. N., KASHEVAROV, A. A., and MEIRMANOV, A. M. (1981), Numerical modelling of simultaneous motion of surface channel and ground waters. Abstracts of the International Conference Numerical Modelling of River, Channel over Land Flow for Water Resources and Environmental Applications, May 4–8, Bratislava, Czechoslovakia, pp. 1–11.
ANTONTSEV, S. N., KASHEVAROV, A. A., and SEMENKO, A., An Iterative Method for Solving a Stationary Problem on Saturated-Unsaturated Filtration in a Hydraulic Approximation, (Dinamika Sploshnoi Sredy, Novosibirsk, Institute of Hydrodynamics, Novosibirsk 1989), Vyp. 90, pp. 3–15.
ANTONTSEV, S. N., KAZHIKHOV, A. V., and MONAKHOV, V. N., Boundary Value Problems in Mechanics of Nonhomogeneous Fluids (North-Holland Publishing Co., Amsterdam, 1990 Translated from original Russian edition: Nauka, Novosibirsk, 1983).
ANTONTSEV, S. N. and MEIRMANOV, A. M., Mathematical models of the coupled motion of surface and ground waters. Mechanics. In Third Congress: Theoretical and Applied Mechanics (Varna, Sept. 13–16, 1977), vol. 1 (Acad. Sci. Bulgaria, Sofia 1977a) pp. 223–228.
ANTONTSEV, S. N. and MEIRMANOV, A. M., Mathematical models of simultaneous motions of surface and ground waters (Novosibirsk State University, Lecture Notes, 1979).
ANTONTSEV, S. N. and MEIRMANOV, A. M. Mathematical questions of the correctness of initial-boundary value problems of a hydraulic model of diffusion waves (Dinamika Sploshnoi Sredy, Institute of Hydrodynamics, Novosibirsk 1977b) 30, pp. 7–34.
ANTONTSEV, S. N. and MEIRMANOV, A. M., Mathematical questions on the correctness of a model of the simultaneous motion of surface and underground water (Dinamika Zhidkosti so Svobod. Granitsami, Institute of Hydrodynamics, Novosibirsk 1977c), Vyp. 31, pp. 5–51.
ANTONTSEV, S. N. and MEIRMANOV, A. M. (1978), Questions of correctness of a model of the simultaneous motion of surface and ground waters, Dokl. Akad. Nauk SSSR, 242, pp. 505–508.
BEAR, J. and VERRUIJT, A., Modelling Groundwater Flow and Pollution. Theory and Applications of Transport in Porous Media, vol. 2. (Kluwer Academic Publisher, Dordrecht, Holland, 1987)
CRANDALL, M. G. and TARTAR, L. (1980), Some relations between nonexpansive and order preserving mappings, Proc. Amer. Math. Soc. 78, 3, 385–390.
CUNNINGHAM, A. and SINCLAIR, P.J. (1979), Application and analysis of coupled surface and groundwater model, J. Hydrol. 43, 129–148.
DALUZ VIEIRA, J.B. (1983), Conditions governing the use of approximations for the Saint-Venant equations for shallow surface water flow, J. Hydrol. 60, 43–58.
DÍAZ, J. I. and JIMENEZ, R., Aplicacio´n de la teorı´a no lineal de semigrupos a un operador pseudodiferencial (Actas del VI CEDYA, Univ. de Granada 1985) pp. 137–142.
Vol. 165, 2008 Channel Level and Ground-Water Flows 1529
DÍAZ, J. I. and TELLO, L., On a parabolic problem with diffusion on the boundary arising in Climatology. International Conference Differential Equations (ed. World Scientific, New Jersey 2005) pp. 1056–1058.
DÍAZ, J. I. and TELLO, L. (2008), On a climate model with a dynamic nonlinear diffusive boundary condition. Discrete and Continuous Dynamical Systems Series S, vol 1, No. 2, 253–262.
DÍAZ, J. I. and THELIN, F. (1994), On a nonlinear parabolic problems arising in some models related to turbulence flows. SIAM J. Math. Anal. 25, 4, 1085–1111.
EPIKHOV, G. (1985), Computation system modelling of water exchange in interactive regime, Vodnue resursy 5, 11–25.
FOWLER, A., Mathematics and the Environment, (Springer-Verlag in press).
KASHEVAROV, A. A. (1998), Mathematical modeling of salt transport by coupled subsurface and surface water flows. J. Appl. Mech. Tech. Phys. 39, 584–591.
KUCHMENT L., DEMIDOV, V., and MOTOVILOV, Y. G., Formation of a River Basin (Nauka, Moscow, Russia 1983).
LUCKHER, L. (1978), Gekoppelte Grundwasser-Oberfla¨chen-Wassermodell (a coupled model of ground and surface waters), Wasserwirt.-Wassertechn. (WWT) 29 (8), 276–278.
MILES, J., Modelling the interaction between aquifers and rivers. In Advances in Water Engineering (Elsevier. Publ., Ltd., London-New York 1985), pp. 94–100.
PHILIP, J. (1969), The Theory of Infiltration, Adv. Hydrosci. 5, pp. 215–296.
POLUBARINOVA-KOCHINA, P. Y., Theory of the Motion of Ground Waters (Nauka, Moscow, Russia 1977).
USENKO, V. and ZLOTNIK V. (1978), Mathematical models and numerical methods in the problems of interconnection of unconfined grounwater and surface water. Proc. of Third Int. Symp., Kiev, 1976, (Part 4, Naukova Dumka, Kiev, USSR, Providence, RI, pp. 108–117).
VASILIEV, O. F., 1987. System modelling of the interaction between surface and ground waters in problems of hydrology. Hydrolog. Sci., 32, pp. 297–311.
|Deposited On:||10 May 2012 08:14|
|Last Modified:||06 Feb 2014 10:18|
Repository Staff Only: item control page