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Article title THE INFLUENCE OF THE THIRD KIND BOUNDARY CONDITIONS ON THE STABILITY OF CONVECTION-DIFFUSION PROBLEM WITH UPWIND APPROXIMATION
Authors I.N. Shabas, L.G. Chikina, A.L. Chikin
Section SECTION II. MATHEMATICAL AND SOFTWARE OF SUPERCOMPUTERS
Month, Year 12, 2014 @en
Index UDC 519.6:532.5
DOI
Abstract The results of the difference approximation of the three-dimensional convection-diffusion problem with boundary conditions of the third kind. Given representation of convection-diffusion operator, leading to M-matrix. We formulate conditions for the stability of the difference scheme convection-diffusion problem upwind approximation of the convective terms. Estimates of solutions based on the maximum principle. For a basis of theoretical research methodology derived mathematical modeling and computational experiment proposed by Academician A.A. Samara and developed in the works of Russian and foreign researchers. When approximating the problem by finite differences is necessary to preserve the main properties of the original differential operators. Therefore, when the spatial approximation of the convection-diffusion equation in which the convective part is recorded in non-divergence form, selected upwind scheme (US). Numerical testing. Numerical testing confirmed vyod that the presence of the boundary conditions of the third kind affects the stability depending on the coefficient of entering into these conditions in the form factor of the free term of a fixed value of the Peclet number.

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Keywords Convection-diffusion problems; antiperspirant difference scheme; boundary conditions of the third kind; the assessment decision.
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