Study of natural convective flows with unstable temperature stratification
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 7, pp. 1289-1303 Cet article a éte moissonné depuis la source Math-Net.Ru

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Flow regimes developing under unstable thermal stratification are studied by analyzing flows in inclined channels heated from the bottom. Regularized Oberbeck–Boussinesq equations written in terms of velocity and pressure are solved by the finite-element method with the software package JoinCAD\FEM. The resulting numerical solutions describe two- and three-dimensional flows in an inclined channel with the end faces held at different temperatures. It is found that coherent structures develop depending on the inclination. The intensity of the convective flows is maximal at a certain value of the inclination.
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P. A. Anan'ev; P. K. Volkov. Study of natural convective flows with unstable temperature stratification. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 7, pp. 1289-1303. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_7_a12/

[1] Ananev P. A., Volkov P. K., Pereverzev A. V., “Issledovanie korrektnosti kraevykh zadach dlya uravnenii Nave-Stoksa v estestvennykh peremennykh”, Matem. modelirovanie, 16:7 (2004), 68–76

[2] Volkov P. K., Pereverzev A. V., “Metod konechnykh elementov dlya resheniya kraevykh zadach regulyarizovannykh uravnenii neszhimaemoi zhidkosti v peremennykh “skorosti-davlenie””, Matem. modelirovanie, 15:3 (2003), 15–28 | Zbl

[3] Volkov P. K., Pereverzev V. A., “Metod konechnykh elementov dlya rascheta nestatsionarnoi konvektsii v neizotermicheskoi zhidkosti v zemnykh i kosmicheskikh usloviyakh”, Tr. regionalnogo konkursa nauchnykh proektov v oblasti estestvennykh nauk, 3, “Eidos”, Kaluga, 2002, 90–100

[4] Volkov P., Pereverzev A., Ananiev P., “Towards a problem-solving system for computational fluid dynamic”, Proc. 8th World Multiconf. Systemics, Cybernetics and Informatics (July 18–21, 2004, Orlando, Florida, USA), v. 9

[5] Kuznetsov B. G., “Ob odnom sposobe approksimatsii uravnenii gidrodinamiki vyazkoi neszhimaemoi zhidkosti”, Dokl. AN SSSR, 213:1 (1973) | Zbl

[6] Temam R., “Une methode d'approximation de Ja Solution des equations de Navier-Stokes”, Bull. Soc. Math. de France, 96 (1968), 115–152 | MR | Zbl

[7] Volkov P. K., “Aspekty beskonechnoi skorosti rasprostraneniya vozmuschenii v sploshnykh sredakh”, Vychisl. tekhnologii, 9:2 (2004), 20–30; Вестн. КазНУ, 42:3

[8] Chorin A. J., “A numerical method for solving incompressible viscous flow problems”, J. Comput. Phys., 2 (1967), 12–26 | DOI | Zbl

[9] Fedoseyev A. I., “A Regularization approach to solving the Navier-Stokes equations for problems with boundary layer”, Comput. Fluid Dynamics J., Proc. 8th ISCFD (1999, ZARM, Bremen), 2001, 317–324

[10] Volkov P. K., Pereverzev A. V., “Reshenie regulyarizovannykh uravnenii neszhimaemoi zhidkosti v peremennykh “skorosti-davlenie” metodom konechnykh elementov”, Vychisl. tekhnologii, 7, no. 2, IVT SORAN, Novosibirsk, 2002, 106–113

[11] Smagulov Sh., “Ob odnom nelineinom uravnenii s malym parametrom, approksimiruyuschem uravnenie Nave-Stoksa”, Tr. V Vses. seminara po chisl. metodam mekhan. vyazkoi zhidkosti, v. 1, VTs SO AN SSSR, Novosibirsk, 1975, 123–134 | MR

[12] Segerlind L., Primenenie metoda konechnykh elementov, Mir, M., 1979

[13] Volkov P. K., Pereverzev A. V., “Nelineinaya dinamika neizotermicheskikh zhidkostei v zemnykh i kosmicheskikh usloviyakh”, Tr. regionalnogo konkursa nauchnykh proektov v oblasti estestvennykh nauk, 1, “Eidos”, Kaluga, 2000, 11–24

[14] Fedoseev A. I., Bessonov O. A., “Effektivnyi podkhod k resheniyu zadach mekhaniki vyazkoi zhidkosti v metode konechnykh elementov”, Chisl. metody v zadachakh teplo- i massoobmena, IPMekhan. RAN, M., 1997, 67–86

[15] Petukhov B. S., Teploobmen i soprotivlenie pri laminarnom techenii zhidkosti v trubakh, Energiya, M., 1967

[16] Petukhov B. C., Polyakov A. F., Teploobmen pri smeshannoi turbulentnoi konvektsii, Nauka, M., 1986 | Zbl

[17] Luciano M. de Socio, “Laminar free convection around horizontal circular cylinders”, J. Heat Mass Transfer, 26:11 (1983), 1669–1677 | DOI

[18] Kuehn T. H., Goldshtein R. J., “Correlating equations for natural convection heat transfer between horizontal cylinders”, Internat. J. Heat Mass Transfer, 19:10 (1976), 1127–1134 | DOI

[19] Polezhaev V. I., Bune A. B., Verezub H. A. i dr., Matematicheskoe modelirovanie konvektivnogo teplomassoobmena na osnove uravnenii Nave-Stoksa, Nauka, M., 1987 | MR

[20] Xia C., Murthy J. Y., Marthur S. R., “Finite volume computations of buoyancy-driven flow in a cubical cavity: A benchmarking exercise”, ICHMT 2-nd Internat. Symp. on Advanced Comput. Heat Transfer, v. 2, Palm Cove, Quennsland, Australia, 2001, 1345–1350

[21] Kejeres S., Gunarjo S. B., Hanjalic K., “Natural convection in an air-filled cubical cavity under different angles of inclination: A benchmark study”, ICHMT 2-nd Internat. Symp. Advanced in Comput. Heat Transfer, v. 2, Palm Cove, Quennsland, Australia, 2001, 1357–1364

[22] Leong W. H., Hollands K. G. T., Brunger A. P., “Experimental Nusselt numbers for a cubical-cavity benchmark problem in natural convection”, Internat. J. Heat Mass Transfer, 42 (1999), 1979–1989 | DOI

[23] Kirdyashkin A. G., Polezhaev V. I., Fedyushkin A. I., “Teplovaya konvektsiya v gorizontalnom sloe pri bokovom podvode tepla”, Zh. prikl. mekhan. i tekhn. fiz., 1983, no. 6, 122–128

[24] Hurle D. T. J., Jakeman K., Johnson C. P., “Convective temperature oscillations in molten galium”, J. Fluid Mech., 64:3 (1974), 565–576 | DOI

[25] Volkov P. K., “Podobie v zadachakh gidromekhaniki nevesomosti”, Uspekhi fiz. nauk, 168:12 (1998), 1323–1329

[26] Khristov Kh. I., Nartov V. P., Tochechnye sluchainye funktsii i krupnomasshtabnaya turbulentnost, SO Nauka, Novosibirsk, 1992 | MR | Zbl