Geodesic
Difference method for calculating the heat flux at an inaccessible boundary in the problem of heat conduction
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 3, pp. 125-141

Voir la notice de l'article provenant de la source Math-Net.Ru

The continuation problem for the heat equation is considered. Determining the heat flux at an inaccessible boundary reduces to an inverse problem. For the numerical solution of the inverse problem, an implicit difference scheme is used. At each time step, for the difference analogue of the elliptic equation, the heat flux at the inaccessible boundary is calculated by an economical direct method. The proposed algorithm significantly expands the range of tasks to be solved and can be used for creation of devices capable of real-time determination of the heat flux on inaccessible measurements of parts of inhomogeneous structures. For example, to determine the heat flux on the internal radius of a pipe made of various materials.
Keywords: heat conduction problem, inverse problem, heat flux, inaccessible boundary, mathematical model, numerical solution, direct method.
Mots-clés : discrete analogue 
@article{SJIM_2023_26_3_a9,
     author = {S. B. Sorokin},
     title = {Difference method for calculating the heat flux at an inaccessible boundary in the problem of heat conduction},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {125--141},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2023_26_3_a9/}
}
TY  - JOUR
AU  - S. B. Sorokin
TI  - Difference method for calculating the heat flux at an inaccessible boundary in the problem of heat conduction
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2023
SP  - 125
EP  - 141
VL  - 26
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2023_26_3_a9/
LA  - ru
ID  - SJIM_2023_26_3_a9
ER  - 
%0 Journal Article
%A S. B. Sorokin
%T Difference method for calculating the heat flux at an inaccessible boundary in the problem of heat conduction
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2023
%P 125-141
%V 26
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2023_26_3_a9/
%G ru
%F SJIM_2023_26_3_a9
S. B. Sorokin. Difference method for calculating the heat flux at an inaccessible boundary in the problem of heat conduction. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 3, pp. 125-141. http://geodesic.mathdoc.fr/item/SJIM_2023_26_3_a9/