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Journal of Automation and Information Sciences
SJR: 0.275 SNIP: 0.59 CiteScore™: 0.8

ISSN Druckformat: 1064-2315
ISSN Online: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v42.i6.50
pages 67-83

On Construction of Finite-Dimensional Mathematical Model of Convection−Diffusion Process with Usage of the Petrov−Galerkin Method

Nikolay N. Salnikov
Institute of Space Research of National Academy of Sciences of Ukraine and National Space Agensy of Ukraine, Kyiv, Ukraine
Sergey V. Siryk
National Technical University of Ukraine "Kyiv Polytechnic Institute"
Igor A. Tereshchenko
National Technical University of Ukraine "Kiev Polytechnic Institute", Kiev


We proposed technique of construction of piecewise-polynomial weighting functions for the Petrov−Galerkin method in two-dimensional domain. The form of these functions is defined by finite number of variable parameters, connected with grid edges. We consider several variants of selection of these parameters depending on the modulus and direction of the vector of advection rate. The method of construction of finite-dimensional model of nonstationary process of convection-diffusion for arbitrary domain in the form of system of ordinary differential equations was proposed. Accuracy of the obtained model is ascertained by comparison of numerical and analytical solutions of a testing problem.

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