Geodesic
Dimension reduction in fluid dynamics equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 8, pp. 1518-1530 
V. B. Akkerman; M. L. Zaytsev. Dimension reduction in fluid dynamics equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 8, pp. 1518-1530. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a13/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A method for transforming the Euler and Navier–Stokes equations and a complete system of fluid dynamics equations in three dimensions to a closed system on any moving surface is proposed. As a result, for an arbitrary geometric configuration, the dimension of the equations is reduced by one, which makes them convenient for numerical simulation. The general principles of the method are described, and verifying examples are presented.

[1] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1966 | MR | Zbl

[2] Landau L. D., Lifshits E. M., Teoreticheskaya fizika, v. VI, Gidrodinamika, Nauka, M., 1986 | MR

[3] Williams F. A., Combustion theory, Benjamin, CA, 1985

[4] Zeldovich Ya. B., Barenblatt G. I., Librovich V. B., Makhviladze G. M., The mathematical theory of combustion and explosion, Consultants Bureau, New York, 1985 | MR

[5] Samarskii A. A., Popov Yu. P., Raznostnye metody resheniya zadach gazovoi dinamiki, Nauka, M., 1980 | MR

[6] Bychkov V. V., “Nonlinear equation for a curved stationary flame and the flame velocity”, Phys. Fluids, 10 (1998), 2091 | DOI | MR | Zbl

[7] Bychkov V., Zaytsev M., Akkerman V., “Coordinate-free description of corrugated flames with realistic gas expansion”, Phys. Rev. E, 68 (2003), 026312 | DOI

[8] Zaitsev M. L., Akkerman V. B., “K nelineinoi teorii dvizheniya poverkhnostei gidrodinamicheskikh razryvov”, Zh. eksperim. i teor. fiz., 135:4 (2009), 800–819 | MR

[9] Sivashinsky G. I., “Nonlinear analysis of hydrodynamics instability in laminar flames. I: Derivation of basic equations”, Acta Astronaut., 4:11–12 (1977), 1177–1206 | DOI | MR | Zbl

[10] Frankel M., “An equation of surface dynamics modeling flame fronts as density discontinuities in potential flows”, Phys. Fluids A, 2 (1990), 1879 | DOI | MR | Zbl

[11] Korenev G. V., Tenzornoe ischislenie, MFTI, M., 1996

[12] Ckhouten Ya. A., Tenzornyi analiz dlya fizikov, Nauka, M., 1965

[13] Pobedrya B. E., Lektsii po tenzornomu analizu, Izd-vo MGU, M., 1986 | Zbl

[14] Fedoryuk M. V., Obyknovennye differentsialnye uravneniya, Lan, SPb., 2003

[15] Polyanin A. D., Zaitsev V. F., Spravochnik po nelineinym uravneniyam matematicheskoi fiziki. Tochnye resheniya, Fizmatlit, M., 2002 | MR

[16] Travnikov O. Yu., Bychkov V. V., Liberman M. A., “Numerical studies of flames in wide tubes. Stability limits of curved stationary flames”, Phys. Rev. E, 61 (2000), 468–474 | DOI

[17] Bychkov V. V., Golberg S. M., Liberman M. A. et al., “Propagation of curved stationary flames in tubes”, Phys. Rev. E, 54 (1996), 3713 | DOI

[18] Kadowaki S., “The influence of hydrodynamic instability on the structure of cellular flames”, Phys. Fluids, 11 (1999), 3426 | DOI | MR | Zbl