Geodesic
Direct numerical simulation of laminar-turbulent flow over a flat plate at hypersonic flow speeds
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 6, pp. 1064-1081 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A method for direct numerical simulation of a laminar-turbulent flow around bodies at hypersonic flow speeds is proposed. The simulation is performed by solving the full three-dimensional unsteady Navier–Stokes equations. The method of calculation is oriented to application of supercomputers and is based on implicit monotonic approximation schemes and a modified Newton–Raphson method for solving nonlinear difference equations. By this method, the development of three-dimensional perturbations in the boundary layer over a flat plate and in a near-wall flow in a compression corner is studied at the Mach numbers of the free-stream of $\mathrm{M} = 5.37$. In addition to pulsation characteristic, distributions of the mean coefficients of the viscous flow in the transient section of the streamlined surface are obtained, which enables one to determine the beginning of the laminar-turbulent transition and estimate the characteristics of the turbulent flow in the boundary layer. 
@article{ZVMMF_2016_56_6_a11,
     author = {I. V. Egorov and A. V. Novikov},
     title = {Direct numerical simulation of laminar-turbulent flow over a flat plate at hypersonic flow speeds},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1064--1081},
     year = {2016},
     volume = {56},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a11/}
}
TY  - JOUR
AU  - I. V. Egorov
AU  - A. V. Novikov
TI  - Direct numerical simulation of laminar-turbulent flow over a flat plate at hypersonic flow speeds
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2016
SP  - 1064
EP  - 1081
VL  - 56
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a11/
LA  - ru
ID  - ZVMMF_2016_56_6_a11
ER  - 
%0 Journal Article
%A I. V. Egorov
%A A. V. Novikov
%T Direct numerical simulation of laminar-turbulent flow over a flat plate at hypersonic flow speeds
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2016
%P 1064-1081
%V 56
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a11/
%G ru
%F ZVMMF_2016_56_6_a11
I. V. Egorov; A. V. Novikov. Direct numerical simulation of laminar-turbulent flow over a flat plate at hypersonic flow speeds. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 6, pp. 1064-1081. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_6_a11/

[1] Fedorov A., “Transition and stability of high-speed boundary layers”, Annu. Rev. Fluid Mech., 43 (2011), 79–95 | DOI | MR | Zbl

[2] Belotserkovskii O. M., Constructive modeling of structural turbulence and hydrodynamic instabilities, World Scientific, Singapore, 2009 | MR | Zbl

[3] Zhong X., Wang X., “Direct numerical simulation on the receptivity, instability, and transition of hypersonic boundary layers”, Annu. Rev. Fluid Mech., 44 (2012), 527–561 | DOI | MR | Zbl

[4] Egorov I. V., Zaitsev O. L., “Ob odnom podkhode k chislennomu resheniyu dvumernykh uravnenii Nave–Stoksa metodom skvoznogo scheta”, Zh. vychisl. matem. i matem. fiz., 31:2 (1991), 286–299 | MR

[5] Egorov I. V., Ivanov D. V., “Primenenie polnostyu neyavnykh monotonnykh skhem dlya modelirovaniya ploskikh vnutrennikh techenii”, Zh. vychisl. matem. i matem. fiz., 36:12 (1996), 91–107 | MR | Zbl

[6] Sivasubramanian J., Fasel H. F., Transition initiated by a localized disturbance in a hypersonic flat-plate boundary layer, AIAA paper, No 2011-374, 2011

[7] Egorov I. V., Fedorov A. V., Soudakov V. G., “Direct numerical simulation of disturbances generated by periodic suction-blowing in a hypersonic boundary layer”, Theor. Comput. Fluid Dyn., 20:1 (2006), 41–54 | DOI | Zbl

[8] Egorov I. V., Novikov A. V., Fedorov A. V., “Chislennoe modelirovanie stabilizatsii sverkhzvukovogo otryvnogo pogranichnogo sloya poristym pokrytiem”, PMTF, 2007, no. 2, 39–47

[9] Egorov I. V., Novikov A. V., Fedorov A. V., “Chislennoe modelirovanie vozmuschenii otryvnogo techeniya v zakruglennom ugle szhatiya”, Izv. RAN. Mekhan. zhidkosti i gaza, 2006, no. 4, 39–49 | MR

[10] Godunov S. K., “Konechno-raznostnyi metod chislennogo rascheta razryvnykh reshenii uravnenii gazovoi dinamiki”, Matem. sbornik, 47 (1959), 271–291

[11] Godunov S. K., Zabrodin A. V., Ivanov M. Ya., Kraiko A. N., Prokopov G. P., Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki, Nauka, M., 1976 | MR

[12] Roe P. L., “Approximate Reimann solvers, parameter vectors, and difference schemes”, J. Comp. Phys., 43 (1981), 357–372 | DOI | MR | Zbl

[13] Jiang G. S., Shu C. W., “Efficient Implementation of Weighted ENO Schemes”, J. Comput. Phys., 126 (1996), 202–228 | DOI | MR | Zbl

[14] Karimov T. Kh., “O nekotorykh iteratsionnykh metodakh resheniya nelineinykh uravnenii v gilbertovom prostranstve”, Dokl. AN SSSR, 269:5 (1983), 1038–1046 | MR

[15] Saad Y., Shultz M. H., “GMRes: a generalized minimal residual algorithm for solving non symmetric linear systems”, SIAM J. Scient. and Statist. Comp., 7:3 (1986), 856–869 | DOI | MR | Zbl

[16] Babaev I. Yu., Bashkin V. A., Egorov I. V., “Chislennoe reshenie uravnenii Nave-Stoksa s ispolzovaniem iteratsionnykh metodov variatsionnogo tipa”, Zh. vychisl. matem. i matem. fiz., 34:11 (1994), 1693–1703 | MR | Zbl

[17] CFD General Notation System, , 2015 (data obrascheniya: 28.04.2015) http://cgns.org/

[18] Balay S., Brown J., Buschelman K., Gropp W. D., Kaushik D., Knepley M. G., McInnes L. C., Smith B. F., Zhang H., PETSc Web page, , 2015 (data obrascheniya: 20.09.2015) http://www.mcs.anl.gov/petsc