Geodesic
Numerical reconstruction of the boundary heat flow for stationary heat convection equations
Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 4, pp. 111-119.

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

A numerical algorithm is proposed for solving the inverse problem for the stationary heat convection equations based on the constrained minimization methods. This algorithm is applied for estimating the heat flow on a part of the boundary from the measured values of the temperature or the velocity vector in the flow domain.
Keywords: heat convection, inverse problem, minimization problem, numerical method. 
@article{SJIM_2014_17_4_a10,
     author = {D. A. Tereshko},
     title = {Numerical reconstruction of the boundary heat flow for stationary heat convection equations},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {111--119},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2014_17_4_a10/}
}
TY  - JOUR
AU  - D. A. Tereshko
TI  - Numerical reconstruction of the boundary heat flow for stationary heat convection equations
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2014
SP  - 111
EP  - 119
VL  - 17
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2014_17_4_a10/
LA  - ru
ID  - SJIM_2014_17_4_a10
ER  - 
%0 Journal Article
%A D. A. Tereshko
%T Numerical reconstruction of the boundary heat flow for stationary heat convection equations
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2014
%P 111-119
%V 17
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2014_17_4_a10/
%G ru
%F SJIM_2014_17_4_a10
D. A. Tereshko. Numerical reconstruction of the boundary heat flow for stationary heat convection equations. Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 4, pp. 111-119. http://geodesic.mathdoc.fr/item/SJIM_2014_17_4_a10/

[1] Alifanov O. M., Obratnye zadachi teploobmena, Mashinostroenie, M., 1988

[2] Gunzburger M. D., Hou L., Svobodny T. P., “The approximation of boundary control problems for fluid flows with an application to control by heating and cooling”, Comput. Fluids, 22 (1993), 239–251 | DOI | MR | Zbl

[3] Ito K., Ravindran S. S., “Optimal control of thermally convected fluid flows”, SIAM J. Sci. Comput., 19:6 (1998), 1847–1869 | DOI | MR | Zbl

[4] Alekseev G. V., “Razreshimost statsionarnykh zadach granichnogo upravleniya dlya uravnenii teplovoi konvektsii”, Sib. mat. zhurn., 39:5 (1998), 982–998 | MR | Zbl

[5] Lee H.-C., Imanuvilov O. Yu., “Analysis of optimal control problems for the 2-D stationary Boussinesq equations”, J. Math. Anal. Appl., 242 (2000), 191–211 | DOI | MR | Zbl

[6] Alekseev G. V., Tereshko D. A., Analiz i optimizatsiya v gidrodinamike vyazkoi zhidkosti, Dalnauka, Vladivostok, 2008

[7] Alekseev G. V., Optimizatsiya v statsionarnykh zadachakh teplomassoperenosa i magnitnoi gidrodinamiki, Nauch. mir, M., 2010

[8] Alekseev G. V., Tereshko D. A., “Ekstremalnye zadachi granichnogo upravleniya dlya statsionarnoi modeli teplovoi konvektsii”, Dokl. AN, 430:2 (2010), 173–178 | MR | Zbl

[9] Korotkii A. I., Kovtunov D. A., “Optimalnoe upravlenie teplovoi konvektsiei”, Tr. IMM UrO RAN, 16, no. 5, 2010, 103–112

[10] Alekseev G. V., Tereshko D. A., “Dvukhparametricheskie ekstremalnye zadachi granichnogo upravleniya dlya statsionarnykh uravnenii teplovoi konvektsii”, Zhurn. vychisl. matematiki i mat. fiziki, 51:9 (2011), 1645–1664 | MR | Zbl

[11] Park H. M., Chung O. Y., “On the solution of an inverse natural convection problem using various conjugate gradient methods”, Internat. J. Numer. Methods Engrg., 47 (2000), 821–842 | 3.0.CO;2-K class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | Zbl

[12] Wong J. C.-F., Yuan P., “A FE-based algorithm for the inverse natural convection problem”, Internat. J. Numer. Methods Fluids, 68 (2012), 48–82 | DOI | MR | Zbl