TY - GEN
T1 - Special spline approximation for the solution of the non-stationary 3-D mass transfer problem
AU - Kangro, Ilmārs
AU - Kalis, Harijs
AU - Teirumnieka, Ērika
AU - Edmunds, Teirumnieks
N1 - Publisher Copyright:
© 2021 Ilmārs Kangro, Harijs Kalis, Ērika Teirumnieka, Edmunds Teirumnieks. Published by Rezekne Academy of Technologies.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - 3-D mass transfer problem
KW - Analytical solution
KW - Conservative averaging method
KW - Hyperbolic type splines
UR - http://journals.rta.lv/index.php/ETR/article/view/6577/5343
UR - https://www.scopus.com/pages/publications/85118637024
U2 - 10.17770/etr2021vol2.6577
DO - 10.17770/etr2021vol2.6577
M3 - Conference paper
VL - 2
T3 - Vide. Tehnologija. Resursi - Environment, Technology, Resources
SP - 69
EP - 73
BT - Vide. Tehnoloģija. Resursi : XIII starptautiskās zinātniski praktiskās konferences materiāli, 2021. gada 17.-18. jūnijs = Environment. Technology. Resources : Proceedings of the 13th International Scientific and Practical Conference, June 17-18, 2021
ER -