"A parallel implementation of sediment transport and bottom surface reconstruction problems on the basis of higher-order difference schemes"
Sukhinov A.I., Chistyakov A.E., Semenyakina A.A., and Nikitina A.V.

Discrete analogs of convective and diffusive transport operators of the fourth order of accuracy are studied in the case of partially filled cells. The numerical results obtained when solving the sediment transport problem on the basis of difference schemes of the second and fourth orders of accuracy are compared. These results show that the accuracy of the solutions to the diffusion problem and the convection-diffusion problem increases by a factor of 66.7 and 48.7, respectively. A library of two-layer iterative methods is built to solve the two-dimensional convection-diffusion problem on the basis of higher-order schemes for nine-diagonal difference equations on a multiprocessor computer system. An algorithm is proposed to reconstruct the submarine bottom topography on the basis of hydrographic information (the water depth at a number of points or contour levels) and its numerical implementation is performed. The proposed method is used to draw a map of the bottom relief of the Azov sea.

Keywords: sediment transport, bottom relief, parallel algorithms, higher-order difference schemes, diffusion-convection problem, distributed computing.

  • Sukhinov A.I. – Chekhov Taganrog State Pedagogical Institute, Faculty of Physics, Mathematics and Informatics; ulitsa Initsiativnaya 48, Taganrog, 347936, Russia; Dr. Sci., Professor, Dean of Faculty, e-mail: sukhinov@gmail.com
  • Chistyakov A.E. – Southern Federal University, Institute of Computer Technologies and Information Security; pereulok Nekrasovskii 44, Taganrog, 347922, Russia; Ph.D., Associate Professor, e-mail: cheese_05@mail.ru
  • Semenyakina A.A. – Southern Federal University, Institute of Computer Technologies and Information Security; pereulok Nekrasovskii 44, Taganrog, 347922, Russia; Graduate Student, e-mail: j.a.s.s.y@mail.ru
  • Nikitina A.V. – Southern Federal University, Institute of Computer Technologies and Information Security; pereulok Nekrasovskii 44, Taganrog, 347922, Russia; Ph.D., Associate Professor, e-mail: nikitina.vm@mail.ru