Numerical modeling of the fractional-differential dynamics of the filtration-convective diffusion on the base of parallel algorithms for cluster systems

1Bogaenko, VA, 1Bulavatsky, VM
1V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2017, 1:21-28
Section: Information Science and Cybernetics
Language: Russian

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
  1. Lavryk V.I., Nikiforovich N.A. Mathematical modelling in hydroecologic studies, Kiev: Fitosotsiotsentr, 1998 (in Russian).
  2. Gorenflo R., Mainardi F. Fractals and Fractional Calculus in Continuum Mechanics, Wien: Springer, 1997: 223-276.
  3. Podlubny I. Fractional differential equations, New York: Academic Press, 1999.
  4. Bulavatsky V.M. Cybern. Syst. Anal., 2012, 48, No 6: 861-869.
  5. Bulavatsky V.M. J. Autom. Inform. Sci., 2012, 44, No 2: 13-22.
  6. Sobolev S.L. Physics-Uspekhi, 1997, 40, No 10: 1043-1054.
  7. Compte A.,Metzler R. J. Phus.A.: Math. Gen., 1997, 30: 7277-7289.
  8. Polubarinova-Kochina P.Ia. The theory of groundwater movement, Moscow: Nauka, 1977 (in Russian).
  9. Samarskij A.A. The theory of difference schemes, Moscow: Nauka, 1977 (in Russian).
  10. Zhang W., Cai X., Holm S. Comput. Math. Appl., 2014, 67: 164-171.
  11. Bogaenko V.A., Bulavatsky V.M., Skopetsky V.V. Control System and Computers, 2008, No 5: 18-23 (in Russian).
  12. Bogaenko V.A., Bulavatsky V.M., Skopetsky V.V. Control System and Computers, 2009, No 4: 60-66 (in Russian).