Electronic Scientific Journal
 
Diagnostics, Resource and Mechanics 
         of materials and structures
Рус/Eng  

 

advanced search

IssuesAbout the JournalAuthorContactsNewsRegistration

All Issues

All Issues
 
2024 Issue 4
 
2024 Issue 3
 
2024 Issue 2
 
2024 Issue 1
 
2023 Issue 6
 
2023 Issue 5
 
2023 Issue 4
 
2023 Issue 3
 
2023 Issue 2
 
2023 Issue 1
 
2022 Issue 6
 
2022 Issue 5
 
2022 Issue 4
 
2022 Issue 3
 
2022 Issue 2
 
2022 Issue 1
 
2021 Issue 6
 
2021 Issue 5
 
2021 Issue 4
 
2021 Issue 3
 
2021 Issue 2
 
2021 Issue 1
 
2020 Issue 6
 
2020 Issue 5
 
2020 Issue 4
 
2020 Issue 3
 
2020 Issue 2
 
2020 Issue 1
 
2019 Issue 6
 
2019 Issue 5
 
2019 Issue 4
 
2019 Issue 3
 
2019 Issue 2
 
2019 Issue 1
 
2018 Issue 6
 
2018 Issue 5
 
2018 Issue 4
 
2018 Issue 3
 
2018 Issue 2
 
2018 Issue 1
 
2017 Issue 6
 
2017 Issue 5
 
2017 Issue 4
 
2017 Issue 3
 
2017 Issue 2
 
2017 Issue 1
 
2016 Issue 6
 
2016 Issue 5
 
2016 Issue 4
 
2016 Issue 3
 
2016 Issue 2
 
2016 Issue 1
 
2015 Issue 6
 
2015 Issue 5
 
2015 Issue 4
 
2015 Issue 3
 
2015 Issue 2
 
2015 Issue 1

 

 

 

 

 

A. L. Kazakov, L. F. Spevak, O. A. Nefedova

SIMULTENIOUS APPLICATION OF THE BOUNDARY ELEMENT METHOD AND THE POWER SERIES METHOD FOR SOLVING A TWO-DIMENSIONAL PROBLEM OF HEAT WAVE MOTION

DOI: 10.17804/2410-9908.2017.6.006-015

The paper develops numerical solution methods for heat conduction boundary value problems for the case of the power dependence of the heat conductivity factor on temperature. Besides heat distribution in space, it describes filtration of a polytropic gas in a porous medium. A distinctive feature of this equation is the degeneration of its parabolic type when the required function becomes zero, whereupon the equation acquires some properties typical of first-order equations. Particularly, in some cases, it proves possible to substantiate theorems of the existence and uniqueness of heat-wave type solutions for it. A numerical method using the advantages of the power series method and the boundary element method is proposed for the solution of the boundary value problem with a specified heat wave front. Simultaneous application of the two methods allows the accuracy of the numerical solution to be increased. A program has been developed from the proposed method. Test examples are considered.

Acknowledgments: K.Program of UB RAS, project № 15-7-1-17 grant of the RFBR, project № 16-01-00608

Keywords: nonlinear heat conduction equation, power series, boundary element method, computational experiment

References:

  1. Vazquez J.L. The Porous Medium Equation: Mathematical Theory. Clarendon Press, Oxford, 2007, 648 р. ISBN-10: 0198569033, ISBN-13: 978-0198569039.
  2. Samarsky A.A., Galaktionov V.A., Kurdyumov S.P. Mikhailov A.P. Rezhimy s obostreniem v zadachakh dlya nelineinykh parabolicheskikh uravneniy [Regimes with Peaking in Prob-lems for Quasilinear Parabolic Equations]. Moscow, Nauka Publ., 1987, 476 p. (In Russian).
  3. Sidorov A.F. In: Izbrannye Trudy: Matematika. Mekhanika [Selected Works: Mathematics. Mechanics]. Moscow, Fizmatlit Publ., 2001, 576 p. (In Russian). ISBN 5-9221-0103-Х.
  4. Kazakov A.L., Spevak L.F. Numerical and analytical studies of a nonlinear parabolic equation with boundary conditions of a special form. Applied Mathematical Modelling, 2013, vol. 37, iss. 10–11, pp. 6918–6928. DOI: 10.1016/j.apm.2013.02.026
  5. Kazakov A.L., Spevak L.F. An analytical and numerical study of a nonlinear parabolic equation with degeneration for the cases of circular and spherical symmetry. Applied Mathematical Modelling, 2015, vol. 40, iss. 2, pp. 1333–1343. DOI: 10.1016/j.apm.2015.06.038
  6. Spevak L.F., Nefedova O.A. Solving a two-dimensional nonlinear heat conduction equation with degeneration by the boundary element method with the application of the dual reci-procity method. In: AIP Conference Proceedings, 2016, vol. 1785, iss. 1, pp. 040077. Available at: http://doi.org/10.1063/1.4967134
  7. Kazakov A.L., Spevak L.F., Nefedova O.A. Solution of a Two-Dimensional Problem on the Motion of a Heat Wave Front with the Use of Power Series and the Boundary Element Method. Izvestiya IGU. Seriya Matematika. Mekhanika, 2016, Vol. 18, pp. 21–37 (In Russian).
  8. Brebbia C.A., Telles J.F.C., Wrobel L.C. Boundary Element Techniques. Springer-Verlag, Berlin, Neidelberg, New-York, Tokyo, 1984, 466 р. ISBN: 978-3-642-48862-7 (Print), 978-3-642-48860-3 (Online). DOI: 10.1007/978-3-642-48860-3
  9. Fedotov V.P., Spevak L.F. One approach to the derivation of exact integration formulae in the boundary element method. Engineering Analysis with Boundary Elements, 2008, vol. 32, no. 10, pp. 883–888. DOI: 10.1016/j.enganabound.2008.03.001
  10. Nardini D., Brebbia C.A. A New Approach to Free Vibration Analysis using Boundary El-ements. Applied Mathematical Modelling, 1983, vol. 7, no. 3, pp. 157–162. DOI: 10.1016/0307-904X(83)90003-3


PDF      

Article reference

Kazakov A. L., Spevak L. F., Nefedova O. A. Simultenious Application of the Boundary Element Method and the Power Series Method for Solving a Two-Dimensional Problem of Heat Wave Motion // Diagnostics, Resource and Mechanics of materials and structures. - 2017. - Iss. 6. - P. 6-15. -
DOI: 10.17804/2410-9908.2017.6.006-015. -
URL: http://eng.dream-journal.org/issues/content/article_151.html
(accessed: 10/11/2024).

 

impact factor
RSCI 0.42

 

MRDMS 2024
Google Scholar


NLR

 

Founder:  Institute of Engineering Science, Russian Academy of Sciences (Ural Branch)
Chief Editor:  S.V. Smirnov
When citing, it is obligatory that you refer to the Journal. Reproduction in electronic or other periodicals without permission of the Editorial Board is prohibited. The materials published in the Journal may be used only for non-profit purposes.
Contacts  
 
Home E-mail 0+
 

ISSN 2410-9908 Registration SMI Эл № ФС77-57355 dated March 24, 2014 © IMACH of RAS (UB) 2014-2024, www.imach.uran.ru