Abstract
A mathematical model is developed for the dynamic analysis of nonisothermal, locally nonequilibrium seepage of salt solutions. The corresponding nonlinear boundary-value problem is formulated, an algorithm for its approximate solution is presented, and results of the numerical solution are given.
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M. M. Khasanov and G. T. Bulgakova, Nonlinear and Nonequilibrium Effects in Geologically Complex Media [in Russian], Inst. Komp. Issled., Moscow–Izhevsk (2003).
V. M. Bulavatskii and V. V. Skopetskii, “System approach to mathematical modeling of filtration consolidation,” Cybern. Syst. Analysis, 42, No. 6, 831–838 (2006).
V. M. Bulavatsky and V. V. Skopetskii, “Mathematical modeling of the dynamics of consolidation processes with relaxation effects,” Cybern. Syst. Analysis, 44, No. 6, 840–846 (2008).
V. M. Bulavatsky, Yu. G. Krivonos, and V. V. Skopetsky, Nonclassical Mathematical Models of Heat and Mass Transfer [in Ukrainian], Naukova Dumka, Kyiv (2005).
A. P. Vlasyuk and P. M. Martynyuk, Mathematical Modeling of Soil Consolidation during the Seepage of Salt Solutions [in Ukrainian], Vydavn. UDUVGP, Rivne (2004).
A. Ya. Bomba, V. M. Bulavatsky, and V. V. Skopetsky, Nonlinear Mathematical Models of Geohydrodynamic Processes [in Ukrainian], Naukova Dumka, Kyiv (2007).
A. P. Vlasyuk and P. M. Martynyuk, Mathematical Modeling of Soil Consolidation during the Seepage of Salt Solutions under Nonisothermal Conditions [in Ukrainian], Vydavn. UDUVGP, Rivne (2008).
V. V. Skopetsky and V. M. Bulavatsky, “Mathematical modeling of seepage consolidation of rock masses saturated with salt solutions under conclusions of relaxation filtration,” Dop. NANU, No. 2, 55–61 (2006).
V. M. Bulavatsky and V. V. Skopetsky, “A nonisothermal consolidation mathematical model of geoinformatics,” J. Autom. Inform. Sci., 42, Issue 12, 1–12 (2010).
V. M. Bulavatsky and V. V. Skopetsky, “Approximate solution of one dynamic problem of geoinformatics,” J. Autom. Inform. Sci., 42, Issue 5, 1–11 (2010).
G. I. Barenblatt, V. N. Entov, and V. M. Ryzhik, Motion of Fluids and Gases in Natural Strata [in Russian], Nedra, Moscow (1984).
I. I. Lyashko, L. I. Demchenko, and G. E. Mistetskii, Numerical Solution of Problems of Heat and Mass Transfer in Porous Media [in Russian], Naukova Dumka, Kyiv (1991).
N. O. Virchenko and V. Ya. Rybak, Fundamentals of Fractional Integro-Differentiation [in Ukrainian], Zadruga, Kyiv (2007).
A. M. Nakhushev, Fractional Calculus and its Application [in Russian], Fizmatlit, Moscow (2003).
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives and some of their Applications [in Russian], Nauka i Tekhnika, Minsk (1987).
A. A. Chikrii and I. I. Matichin, “An analog of the Cauchy formula for linear systems of arbitrary fractional order,” Dop. NANU, No. 1, 50–55 (2007).
A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam (2006).
R. Gorenflo and F. Mainardi, “Fractional calculus: Integral and differential equations of fractional order,” in: A. Carpinteri and F. Mainardi (eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer-Verlag, Wien (1997), pp. 223–276.
I. Podlubny, Fractional Differential Equations, Acad. Press, New York (1999).
G. N. Polozhii, Numerical Solution of Two-Dimensional and Three-Dimensional Boundary-Value Problems of Mathematical Physics and Discrete-Argument Functions [in Russian], Vyshcha Shkola, Kyiv (1962).
A. A. Samarskii, Theory of Difference Schemes [in Russian], Nauka, Moscow (1977).
F. I. Taukenova and M. N. Shkhanukov-Lafishev, “Difference methods for solving boundary-value problems for fractional differential equations,” Comp. Math. Math. Physics, 46, No. 10, 1785–1795 (2006).
V. Ya. Arsenin, Mathematical Physics. Fundamental Equations and Special Functions [in Russian], Nauka, Moscow (1966).
A. A. Samarskii and P. N. Vabishchevich, Computational Heat Transfer, Vol. 2, Wiley, New York (1995).
N. S. Bakhvalov, N. P. Zhidkov, and G. M. Kobel’kov, Numerical Methods [in Russian], Nauka, Moscow (1987).
V. I. Krylov and A. T. Shul’gina, Numerical Integration: A Reference Book [in Russian], Nauka, Moscow (1966).
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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 79–88, November–December 2011.
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Bulavatsky, V.M. Nonclassical mathematical model in geoinformatics to solve dynamic problems for nonequilibrium nonisothermal seepage fields. Cybern Syst Anal 47, 898–906 (2011). https://doi.org/10.1007/s10559-011-9369-4
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DOI: https://doi.org/10.1007/s10559-011-9369-4