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Journal of Automation and Information Sciences
SJR: 0.232 SNIP: 0.464 CiteScore™: 0.27

ISSN Imprimir: 1064-2315
ISSN On-line: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v51.i5.20
pages 16-29

Computer Simulation Based on Non-local Model of the Dynamics of Convective Diffusion of Soluble Substances in the Underground Filtration Flow under Mass Exchange Conditions

Vsevolod A. Bohaienko
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
Vladimir M. Bulavatskiy
V. M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev, Ukraine

RESUMO

The paper deals with the problem of modeling the dynamics of locally nonequilibrium in time process of soluble substances convective diffusion under the conditions of flat-vertical steady-state groundwater filtration with free surface taking into account the presence of phase-to-phase mass transfer. The urgency of solving such problem is due, in particular, to the need for development of measures for soil flushing as well as desalination and purification of groundwater from pollutants. For mathematical modeling of the corresponding transfer process in media with a property of temporal nonlocality this paper used the apparatus of fractional-order integro-differentiation. The corresponding nonlinear fractional differential model of the migration process has been developed using Caputo-Katugampola generalized fractional order derivative of a function with respect to another function which allows us in a sense to control the modeling process. In this model the nonequilibrium convection-diffusion process in a porous medium is considered under conditions of mass exchange. For the proposed mathematical model the formulation of the corresponding boundary value problem was carried out and the technique for its numerical solution was developed. This technique is based on a preliminary transition using the conformal mapping method from the physical How domain to the domain of complex potential which is canonical. The algorithm for approximate solution of the considered boundary value problem in the domain of complex potential is based on a linearized version of the locally one-dimensional difference scheme of A.A. Samarsky. The results of computer simulations demonstrate that the value of the exponent in the Caputo-Katugampola derivative significantly affects the simulation results giving both sub-diffusion and super-diffusion patterns of concentration fields distribution. Computational experiments also show that when mass exchange phenomenon is taken into account while modeling pollution propagation from water bodies to soil media it leads to a delay in the concentration front development in a liquid phase. The paper has drawn the conclusions regarding the influence of the mathematical model parameters on the resulting picture of concentration fields formation.

Referências

  1. Lyashko I.I., Demchenko L.I., Mistetskiy G.E., Numerical solution of problems of heat and mass transfer in porous media [in Russian], Naukova dumka, Kiev, 1991.

  2. Polubarinova-Kochina P.Ya., Theory of ground-water motion [in Russian], Nauka, Moscow, 1977.

  3. Bulavatsky V.M., Special boundary value problems of underground hydrodynamics [in Russian], Naukova dumka, Kiev, 1993.

  4. Bomba A.Ya., Bulavatsky V.M., Skopetsky V.V., Nonlinear mathematical models of geohydrodynamics processes [in Ukrainian], Naukova dumka, Kiev, 2007.

  5. Bulavatsky V.M., KryvonosIu.G., Skopetsky V.V., Nonclassical mathematical models of heat and mass transfer processes [in Ukrainian], Naukova dumka, Kiev, 2005.

  6. Khasanov M.M., Bulgakova G.T., Nonlinear and nonequilibrium effects in Theologically complex media [inRussian], Institutkompyuternykh issledovaniy, Moskva-Izhevsk, 2003.

  7. Sobolev S.L., Locally nonequilibrium models of transfer processes, Uspekhifizicheskikh nauk, 1977, 167, No. 10, 1095-1106.

  8. Meylanov M.M., Shibanova M.P., Feature of solving equation of heat transfer in fractional order derivatives, Zhurnal tekhnicheskoy fiziki, 2011, 81, No. 7, 1-6.

  9. Gorenflo R., Mainardi F., Fractional calculus: integral and differential equations of fractional order. Fractals and Fractional Calculus in Continuum Mechanics, Springer Verlag, Wien, 1997, 223-276.

  10. Mainardi F., Fractional calculus and waves in linear viscoelasticity, Imperial College Press, London, 2010.

  11. Podlubny I., Fractional differential equations, Academ. Press, New York, 1999.

  12. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and applications of fractional differential equations, Elsevier, Amsterdam, 2006.

  13. Povstenko Yu., Linear fractional diffusion-wave equation for scientists and engineers, Springer Int. Publ. Switzerland, 2015.

  14. Uchaykin V.V., Method of fractional derivatives [in Russian], Artishok, Ulyanovsk, 2008.

  15. Bulavatsky V.M., Mathematical modeling of dynamics of the process of filtration convective diffusion under the condition of time nonlocality, Journal of Automation and Information Science, 2012, No. 4, 44, 13-22.

  16. Bulavatsky V.M., Kryvonos Iu.G., Mathematical models with a control function for investigation of fractional-differential dynamics of geomigration processes, Mezhdunarodnyi nauchno-tekhnicheskiy zhurnal "Problemy upravleniya i informatiki, 2014, No. 3, 138-147.

  17. VeriginN.N., Vasiliev S.V., KuranovN.R., Methods of predicting salt regimes of soils and ground waters [inRussian], Kolos, Moscow, 1979.

  18. Mistetskiy G.E., Hydro construction. Automated calculation of mass transfer in soils [in Russian], Budivelnyk, Kiev, 1985.

  19. Katugampola U.N., New approach to generalized fractional derivatives, Bui. Math. Anal. Appl., 2014, No. 6, 1-15.

  20. Almeida R.A., Caputo fractional derivative of a function with respect to another function, Communications in Nonlinear Science and Numerical Simulation, 2017, No. 44, 460-481.

  21. VlasyukA.P., OstapchukO.P., Mathematical modeling of salt solutions transfer at filtration of underground waters in soil media [in Ukrainian], NUVGP, Rivne, 2015.

  22. VlasyukA.P., MartynyukP.M., Mathematical modeling of soil consolidation when filtering salt solutions in non-isothermal conditions [in Ukrainian], NUVGP, Rivne, 2008.

  23. Samarsky A. A., Theory of difference schemes [in Russian], Nauka, Moscow, 1977.


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