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Article title PARALLEL REALIZATION SUBSTANCE TRANSPORTATION PROBLEM BASED ON HIGH ACCURACY SCHEMES FOR DIFFUSION-ADVECTION EQUATIONS
Authors L.A. Grigoryan, A.A. Semenyakina
Section SECTION III. THE USE OF SUPERCOMPUTER TECHNOLOGIES
Month, Year 12, 2014 @en
Index UDC 532.5.031
DOI
Abstract In this paper we construct difference analog of the operator of the convective and diffusive transport, having a fourth-order approximation error with respect to the uniform spatial grid step, including, in the case of partially filled cells. The study was conducted in the absence of the influence of the border. Complexity of the structure of difference operators allowed to reach the required local approximation error for internal nodes of the grid, including, in the case of a partially filled grid cells. At the same time it took to increase the demands on the smoothness of the solution. It is assumed that the function solution has continuous derivatives with respect to spatial variables to the fifth order are bounded derivatives – the second order. In contrast to the traditional approach used in the approximation of a function of filling cells, providing an opportunity to improve the accuracy of (smooth) solutions near the boundary stepped form on uniform grids. The numerical comparison of the constructed schemes of the fourth order of accuracy and traditional, having a second-order problem on the test showed significant superiority in accuracy (60–70 times) the proposed approximation on grids, including 100x100 nodes for sufficiently smooth test functions for the solution. Constructed parallel algorithm Seidel method for solving grid convection-diffusion problems, based on the two-dimensional domain decomposition according to one of the coordinate directions with partial overlap (3 knots) subdomains in memory of individual processors, which showed acceptable performance at a relatively small number of processors (a few tens of processors).

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Keywords Diffusion-advection problems; high order difference schemes.
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