SPECIAL HPERBOLIC TYPE APPROXIMATION FOR SOLVING OF 3-D TWO LAYER STATIONARY DIFFUSION PROBLEM

Ilmārs Kangro, Harijs Kalis, Ērika Teirumnieka, Edmunds Teirumnieks

Abstract


In this paper we examine the conservative averaging method (CAM) along the vertical z-coordinate for solving the 3-D boundary-value 2 layers diffusion problem. The special parabolic and hyperbolic type approximation (splines), that interpolate the middle integral values of piece-wise smooth function, is investigated. With the help of these splines the problems of mathematical physics in 3-D with respect to one coordinate are reduced to problems for system of equations in 2-D in every layer. This procedure allows reduce also the 2-D problem to a 1-D problem and the solution of the approximated problem can be obtained analytically. As the practical application of the created mathematical model, we are studying the calculation of the concentration of heavy metal calcium (Ca) in a two-layer peat block.

Keywords


conservative averaging method; finite-difference method; diffusion problem; special splines

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References


.N. S. Bahvalov, N. P. Zhitkov and G. M. Kobelhkov, Numerical methods. M.: Nauka, 1987 (in Russian).

J. Bear, Hydraulic of groundwater. Mc.Graw-Hill Inc., 1979.

A. Buikis, ”The approximation with splines for problems in layered systems,” in Acta Universitatis Latviensis, Vol. 592, Riga, 1994, pp. 135-138 (in Latvian).

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).

C. Henry Edwards and David E. Penny, Differential equations and boundary value problems, computing and modelling. Pearson, Prentice Hal, third edition, 2008 (in Russian).

H. Kalis, A. Buiķis,A. Aboltins and I. Kangro, ”Special Splines of Hyperbolic Type for the Solutions of Heat and Mass Transfer 3-D Problems in Porous Multi-Layered Axial Symmetry Domain,” Mathematical Modelling and Analysis, vol. 22, issue 04, pp. 425-440, 2017.

A. A. Samarskij, Theory of finite difference schemes. M.: Nauka, 1977 (in Russian).

Ē. Teirumnieka, M., Kļaviņš and E. Teirumnieks, ”Major and trace elements in peat from bogs of east Latvia,” in Mires and Peat /Ed. Māris Kļaviņš, Riga: University of Latvia Press, 2010, pp. 115-124.

J. W.Thomas, Numerical partial differential equations. Finite difference methods. New-York: Springer-Verlag, Inc., 1995.




DOI: http://dx.doi.org/10.17770/etr2019vol3.4079

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