Ilmārs Kangro, Harijs Kalis, Ērika Teirumnieka, Edmunds Teirumnieks


In this paper we consider the conservative averaging method (CAM) with special spline approximation for solving the non-stationary 3-D mass transfer problem. The special hyperbolic type spline, which interpolates the middle integral values of piece-wise smooth function is used. With the help of these splines the initial-boundary value problem (IBVP) of mathematical physics in 3-D domain with respect to one coordinate is reduced to problems for system of equations in 2-D domain. This procedure allows reduce also the 2-D problem to a 1-D problem and thus the solution of the approximated problem can be obtained analytically. The accuracy of the approximated solution for the special 1-D IBVP is compared with the exact solution of the studied problem obtained with the Fourier series method. The numerical solution is compared with the spline solution. The above-mentioned method has extensive physical applications, related to mass and heat transfer problems in 3-D domains.



conservative averaging method, 3-D mass transfer problem, hyperbolic type splines, analytical solution

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A. Buikis, ”The analysis of schemes for the modelling same processes of filtration in the underground, ” in Acta Universitatis Latviensis, Vol. 592, Riga, 1994, pp. 25-32 (in Latvian).

J. Crank, The matehematics of diffusion. Calewdon Press. Oxford, 1975.

I. Kangro, H. Kalis, A. Gedroics, Ē. Teirumnieka, E. Teirumnieks, ”On mathematical modelling of metals distribution in peat layers”, ”Mathematical Modelling and Analysis”, vol. 19, issue 4, pp. 568-588, 2014.

E. Teirumnieka, I. Kangro E. Teirumnieks, H. Kalis, A. Gedroics, ”The mathematical modeling of Ca and Fe distribution in peat layers”, Proc. of the 8-th int. Scientific and Practical Conference "Environment. Technology. Resources", Rezekne Higher Education institution, June 20-22, volume 2, pp. 40-47, 2011.

R. Vilums, A. Buikis, ”Transient heat conduction in 3D fuse modelled by conservative averaging method”, Topics in advanced theoretical and applied mechanics. Proceedings of International conference”3rd WSEAS International Conference on Applied and Theoretical Mechanics”, December 14-16, 2007, Puerto de la Cruz, Spain, pp. 54-63.

R. Vilums, A. Rudevics ”Cylindrical model of transient heat conduction in automotive fuse using conservative averaging method”, Applied and computational mathematics, 2nd edition. Proceedings of International conference”13th WSEAS International Conference on Applied Mathematics”, December 15-17, 2008, Puerto de la Cruz, pain, pp. 355-364.

DOI: https://doi.org/10.17770/etr2021vol2.6577


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