Geodesic
Method of local potential for the prediction of stationary flame spread rate
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2010), pp. 87-95 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The problem of the prediction of steady flame spread rate has been studied. Finite element method has been applied to the boundary value problem involving two approaches for deriving the system of algebraic equations: weighted residuals method for differential conservation equation and variational formulation in the form local thermodynamic potential. The detailed numerical algorithm and results of solution's stability and convergence study have been presented.
Keywords: flame spread, stationary state, variational principle, local potential. 
@article{VUU_2010_4_a9,
     author = {A. I. Karpov and A. V. Kudrin},
     title = {Method of local potential for the prediction of stationary flame spread rate},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {87--95},
     year = {2010},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2010_4_a9/}
}
TY  - JOUR
AU  - A. I. Karpov
AU  - A. V. Kudrin
TI  - Method of local potential for the prediction of stationary flame spread rate
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2010
SP  - 87
EP  - 95
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VUU_2010_4_a9/
LA  - ru
ID  - VUU_2010_4_a9
ER  - 
%0 Journal Article
%A A. I. Karpov
%A A. V. Kudrin
%T Method of local potential for the prediction of stationary flame spread rate
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2010
%P 87-95
%N 4
%U http://geodesic.mathdoc.fr/item/VUU_2010_4_a9/
%G ru
%F VUU_2010_4_a9
A. I. Karpov; A. V. Kudrin. Method of local potential for the prediction of stationary flame spread rate. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2010), pp. 87-95. http://geodesic.mathdoc.fr/item/VUU_2010_4_a9/

[1] Karpov A. I., “O formulirovke termodinamicheskogo variatsionnogo printsipa dlya zadachi o statsionarnom rasprostranenii plameni”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2008, no. 3, 61–68

[2] Zeldovich Ya. B., Barenblatt G. I., Librovich V. B., Makhviladze G. M., Matematicheskaya teoriya goreniya i vzryva, Nauka, M., 1980, 478 pp. | MR

[3] Vilyams F. A., Teoriya goreniya, Nauka, M., 1971, 616 pp.

[4] Karpov A. I., “Minimal Entropy Production as an Approach to the Prediction of Stationary Rate of Flame Propagation”, J. Non-Equilib. Thermodyn., 17:1 (1992), 1–9 | DOI | Zbl

[5] de Groot S., Mazur P., Neravnovesnaya termodinamika, Mir, M., 1964, 456 pp.

[6] Glensdorf P., Prigozhin I., Termodinamicheskaya teoriya struktury, ustoichivosti i fluktuatsii, Mir, M., 1973, 280 pp. | MR

[7] Karpov A. I., Bulgakov V. K., “Ob odnom netraditsionnom algoritme rascheta skorosti rasprostraneniya plameni”, Fizika goreniya i vzryva, 26:5 (1990), 137–138

[8] Gerasev A. P., “Neravnovesnaya termodinamika teplovykh voln v sloe katalizatora. Funktsional avtovolnovogo resheniya”, Fizika goreniya i vzryva, 36:3 (2000), 51–59

[9] Shekhter R. S., Variatsionnyi metod v inzhenernykh raschetakh, Mir, M., 1971, 291 pp.

[10] Finlayson B. A., Scriven L. E., “On the Search for Variational Principles”, Int. J. Heat Mass Transfer, 10 (1967), 799–821 | DOI | Zbl

[11] Patankar S., Chislennye metody resheniya zadach teploobmena i dinamiki zhidkosti, Energoatomizdat, M., 1984, 152 pp.

[12] Karpov A. I., Bulgakov V. K., Novozhilov V., “Quantitative estimation of relationship between the state with minimal entropy production and the actual stationary regime of flame propagation”, J. Non-Equilib. Thermodyn., 28:3 (2003), 193–205 | DOI