Title | Numerical modeling of the fractional-differential dynamics of the filtration-convective diffusion on the base of parallel algorithms for cluster systems |
Publication Type | Journal Article |
Year of Publication | 2017 |
Authors | Bogaenko, VA, Bulavatsky, VM |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2017.01.021 |
Issue | 1 |
Section | Information Science and Cybernetics |
Pagination | 21-28 |
Date Published | 1/2017 |
Language | Russian |
Abstract | Within the framework of the fractional-differential mathematical model of an abnormal convective-diffusion process under conditions of a mass-transfer and a plane filtration field, the statement of the conforming two-dimensional non-stationary boundary-value problem is executed, and the finite-difference technique of obtaining its approximated solution, founded on application of a locally one-dimensional method in the field of a complex potential flow is described. The parallel algorithms of solving the problem on cluster systems are designed, the results of their performance testing and the results of numerical experiments on a simulation of the dynamics of the studied process are presented. |
Keywords | abnormal convective-diffusion process, boundary value problems, fractional diffusion equation, mass-transfer, numerical modeling, parallel algorithms, plane-vertical filtration |
- Lavryk V.I., Nikiforovich N.A. Mathematical modelling in hydroecologic studies, Kiev: Fitosotsiotsentr, 1998 (in Russian).
- Gorenflo R., Mainardi F. Fractals and Fractional Calculus in Continuum Mechanics, Wien: Springer, 1997: 223-276. https://doi.org/10.1007/978-3-7091-2664-6_5
- Podlubny I. Fractional differential equations, New York: Academic Press, 1999.
- Bulavatsky V.M. Cybern. Syst. Anal., 2012, 48, No 6: 861-869. https://doi.org/10.1007/s10559-012-9465-0
- Bulavatsky V.M. J. Autom. Inform. Sci., 2012, 44, No 2: 13-22. https://doi.org/10.1615/JAutomatInfScien.v44.i4.20
- Sobolev S.L. Physics-Uspekhi, 1997, 40, No 10: 1043-1054. https://doi.org/10.1070/PU1997v040n10ABEH000292
- Compte A.,Metzler R. J. Phus.A.: Math. Gen., 1997, 30: 7277-7289. https://doi.org/10.1088/0305-4470/30/21/006
- Polubarinova-Kochina P.Ia. The theory of groundwater movement, Moscow: Nauka, 1977 (in Russian).
- Samarskij A.A. The theory of difference schemes, Moscow: Nauka, 1977 (in Russian).
- Zhang W., Cai X., Holm S. Comput. Math. Appl., 2014, 67: 164-171. https://doi.org/10.1016/j.camwa.2013.11.007
- Bogaenko V.A., Bulavatsky V.M., Skopetsky V.V. Control System and Computers, 2008, No 5: 18-23 (in Russian).
- Bogaenko V.A., Bulavatsky V.M., Skopetsky V.V. Control System and Computers, 2009, No 4: 60-66 (in Russian).