Computer modeling of the fractional-differential dynamics of some filtration-consolidation processes

1Bogaenko, VA, 1Bulavatsky, VM
1V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2018, 4:16-24
Section: Information Science and Cybernetics
Language: Russian

Within the framework of models based on the concept of Caputo—Fabrizio fractional derivative, the com puter simulation of the fractional-differential filtration-consolidation dynamics of saltsaturated groundwa ter massifs is performed. The technique to obtain numerical solutions of the corresponding boundaryvalue problems for systems of fractional differential equations of filtration and salt transfer is developed, the approach to the parallelization of the computational process is described, and the results of numerical experiments on modeling the dynamics of the considered process are presented.

Keywords: boundary-value problems, dynamics of filtration-consolidation processes, finite difference solutions, fractional-differential mathematical models, mathematical and computer modelling, mathematical modelling, models with non-singular kernel, parallelization of computations

1. Florin, V. A. (1961). The basis of soil mechanics. V.2. Moscow: Gosstroiizdat (in Russian).
2. Zaretskiy, Ju. K. (1967). The theory of soil consolidation. Moscow: Nauka (in Russian).
3. Shirinkulov, T. Sh. & Zaretskiy, Ju. K. (1986). Creep and consolidation of soils. Tashkent: Fan (in Russian).
4. Vlasiuk, A.P. & Martyniuk, P.M. (2004) Mathematical modelling of soil consolidation under the conditions of salt solutions filtration process. Rivne: UDUVHP (in Ukrainian).
5. Vlasiuk, A. P. & Martyniuk, P. M. (2008). Mathematical modelling of soil consolidation under the conditions of nonisothermal salt solutions filtration process. Rivne: UDUVHP (in Ukrainian).
6. Kilbas, A. A., Srivastava, H. M. & Trujillo, J. J. (2006). Theory and applications of fractional differential equations. Amsterdam: Elsevier.
7. Bulavatsky, V. M. (2011). Mathematical model of geoinformatics for investigation of dynamics for locally nonequilibrium geofiltration processes. J. Autom. Inform. Sci., 43, No. 12, pp. 12-20. doi:
8. Bulavatsky, V. M. (2013). Simulation of dynamics of some locally nonequilibrium geomigration processes on the basis of a fractionaldifferential geoinformation model. J. Autom. Inform. Sci., 45, No. 11, pp. 75-84. doi:
9. Bulavatsky, V. M. & Krivonos, Yu. G. (2012). Mathematical modelling in the geoinformation problem of the dynamics of geomigration under spacetime nonlocality. Cybern. Syst. Anal., 48, No. 4, pp. 539-546. doi:
10. Bulavatsky, V. M. (2014). Fractional differential mathematical models of the dynamics of nonequilibrium geomigration processes and problems with nonlocal boundary conditions. Cybern. Syst. Anal., 50, No. 1, pp. 81-89. doi:
11. Atangana, A. & Alkahtani, B. (2015). New model of groundwater flowing within a confine aquifer: application of Caputo-Fabrizio derivative. Arabian journ. of geosciences, 9, No. 1, pp. 16.
12. Atangana, A. & Baleanu, D. (2017). Caputo-Fabrizio derivative applied to groundwater flow within confined aquifer. J. of Eng. Mech., 143, No. 5, pp. 15. doi:
13. Caputo, M. & Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progress Fract. Diff. Appl., 1, No. 2, pp. 73-85.
14. Samarskij, A. A. (1977). The theory of difference schemes. Moscow: Nauka (in Russian).
15. Zhang, Y., Cohen, J. & Owens, J. D. (2010). Fast Tridiagonal Solvers on the GPU. Proceedings of the 15th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming (PPoPP 2010), pp. 127-136. doi: