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Article title PARALLEL SOLUTION OF THE DIFFUSION-CONVECTION PROBLEMS BASED ON SCHEMES OF HIGH ORDER OF ACCURACY
Authors A.A. Semenyakina
Section SECTION IV. THE APPLICATION OF SUPERCOMPUTER TECHNOLOGIES IN SCIENCE, TECHNOLOGY AND INDUSTRY
Month, Year 11, 2016 @en
Index UDC 519.8
DOI 10.18522/2311-3103-2016-11-132139
Abstract The article is devoted to parallel implementation of the tasks of diffusion-convection, per-formed on multiprocessor computer system of the Southern federal university. Developed schemes of the higher (fourth) order of accuracy that taking into account the partial filling of control cells have been used for solving of problems of hydrophysics for modeling the distribution of contaminants which have a negative influence on the ecological situation of coastal systems. Approximation of the diffusion-convection problem has been performed on the basis of difference schemes of high order of accuracy. Regularized schemes have been used to improve the stability of explicit schemes. The calculation algorithm takes into account the partial filling of cells, devoid of disadvantage associated with a stepped representation of the boundary region in a rectangular grid. The paper presents the model of petroleum products transportation in coastal systems which differs in the consideration of many factors influencing the contaminants distribution in the waters: neutral and no- evaporating pseudofractal oil spills; evaporation of the light fraction; dissolving and spreading of the oil slick; deposition; diffusion; advection and biodegradation. A library of application programs have been developed on the basis of multiprocessor computer system, which includes numerical implementation of two-layer iterative methods of variational type, designed to solve thirteen-diagonal grid equations from discretization diffusion-convection problems. The experimental software has been designed for mathematical modeling of various scenarios of development of ecological conditions in coastal systems on the example of Azov-Black sea basin in case of oil spill. The simulation of the oil and petroleum products distribution was performed during an emergency spill that occurred in the Kerch Strait in November 2007. The methods of decomposition regions for computing time-consuming diffusion-convection tasks have been used in the parallel implementation, taking into account the architecture and parameters of the multiprocessor computer system. The obtained results demonstrate that the developed numerical methods allow improving the accuracy of predictive modeling of pollutant transport in coastal ecosystems, and provide an opportunity to obtain operational forecasts of the ecological state of water bodies in the shortest possible time intervals.

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Keywords Mathematical model; diffusion-convection problem; schemes of high order of accuracy; transport of oil products; library of application programs; multiprocessor computer system.
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