Geodesic
A minimum-stencil difference scheme for computing two-dimensional axisymmetric gas flows: Examples of pulsating flows with instabilities
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 4, pp. 734-753 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A minimum-stencil difference scheme for computing two-dimensional axisymmetric gas flows is described. The scheme is explicit, conservative, and second-order accurate in space and time. The numerical results obtained for pulsating flows and contact discontinuity instabilities are discussed. The mechanisms of flow pulsation and instability generation are described. 
@article{ZVMMF_2009_49_4_a14,
     author = {O. A. Azarova},
     title = {A~minimum-stencil difference scheme for computing two-dimensional axisymmetric gas flows: {Examples} of pulsating flows with instabilities},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {734--753},
     year = {2009},
     volume = {49},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a14/}
}
TY  - JOUR
AU  - O. A. Azarova
TI  - A minimum-stencil difference scheme for computing two-dimensional axisymmetric gas flows: Examples of pulsating flows with instabilities
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 734
EP  - 753
VL  - 49
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a14/
LA  - ru
ID  - ZVMMF_2009_49_4_a14
ER  - 
%0 Journal Article
%A O. A. Azarova
%T A minimum-stencil difference scheme for computing two-dimensional axisymmetric gas flows: Examples of pulsating flows with instabilities
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 734-753
%V 49
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a14/
%G ru
%F ZVMMF_2009_49_4_a14
O. A. Azarova. A minimum-stencil difference scheme for computing two-dimensional axisymmetric gas flows: Examples of pulsating flows with instabilities. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 4, pp. 734-753. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_4_a14/

[1] Lax P. D., Wendroff B., “Systems of conservation laws”, Communs Pure and Appl. Math., 13 (1960), 217–237 | DOI | MR | Zbl

[2] Tolstykh A. I., “O neyavnykh raznostnykh skhemakh tretego poryadka tochnosti dlya mnogomernykh zadach”, Zh. vychisl. matem. i matem. fiz., 16:5 (1976), 1182–1190 | MR | Zbl

[3] Grudnitskii V. G., Prokhorchuk Yu. A., “Odin priem postroeniya raznostnykh skhem s proizvolnym poryadkom approksimatsii differentsialnykh uravnenii v chastnykh proizvodnykh”, Dokl. AN SSSR, 234:6 (1977), 1249–1252 | MR

[4] Belotserkovskii O. M., Grudnitskii V. G., “Issledovanie nestatsionarnykh techenii gaza so slozhnoi vnutrennei strukturoi metodami integralnykh sootnoshenii”, Zh. vychisl. matem. i matem. fiz., 20:6 (1980), 1400–1415 | MR

[5] Belotserkovskii O. M., Grudnitskii V. G., Prokhorchuk Yu. A., “Raznostnaya skhema vtorogo poryadka tochnosti na minimalnom shablone dlya giperbolicheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz., 23:1 (1983), 119–126 | MR

[6] Azarova O. A., Grudnitskii V. G., “Chislennye metody s vydeleniem razryvov dlya rascheta techenii pri lokalizovannom vydelenii energii v zhidkostyakh i gazakh”, Matem. modelirovanie, 4:12 (1992), 9–13

[7] Azarova O. A., “Raznostnaya skhema s vydeleniem razryvov dlya rascheta vzryvnykh techenii v zhidkostyakh i gazakh”, Akustika neodnorodnykh sred, Dinamika sploshnoi sredy, 105, In-t gidrodinamiki SO RAN, Novosibirsk, 1992, 8–14 | MR

[8] Grudnitskii V. G., Podobryaev V. N., “O vzaimodeistvii udarnoi volny s tsilindricheskim rezonatorom”, Zh. vychisl. matem. i matem. fiz., 23:4 (1983), 1008–1011

[9] Baimirov B. M., Grudnitskii V. G., “Chislennoe issledovanie techenii gaza, voznikayuschikh pri “mnogotochechnom” vydelenii energii”, Zh. vychisl. matem. i matem. fiz., 35:2 (1995), 271–281 | MR | Zbl

[10] Azarova O. A., Vlasov V. V., Grudnitskii V. G., Uschapovskii V. A., Issledovanie razlichnykh podkhodov k postroeniyu skhem vysokogo poryadka tochnosti dlya kvazilineinykh evolyutsionnykh uravnenii, Dep. v VINITI. Ser. 0.No 6, 1983

[11] Azarova O. A., “Chislennoe modelirovanie protsessov pri bystrom vydelenii energii v vode”, Algoritmy dlya chisl. issl. razryvnykh techenii, Tr. VTs RAN, M., 1992, 80–98

[12] Farzan F., Knight D., Azarova O., Kolesnichenko Y., Interaction of microwave filament and blunt body in supersonic flow, Paper AIAA-2008-1356, 1–24

[13] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1977 | MR | Zbl

[14] Azarova O. A., Grudnitskii V. G., Kolesnichenko Yu. F., “Chislennoe issledovanie vozdeistviya tonkogo razrezhennogo kanala na sverkhzvukovoe obtekanie tel s klinovidnym vystupom”, Matem. modelirovanie, 17:10 (2005), 104–112 | Zbl

[15] Azarova O. A., “Chislennoe modelirovanie vzaimodeistviya turbulentnosti s udarnoi volnoi v potoke szhimaemogo gaza”, Zh. vychisl. matem. i matem. fiz., 44:3 (2004), 543–552 | MR | Zbl

[16] Georgievskii P. Yu.,Levin V. A., “Sverkhzvukovoe obtekanie tel pri nalichii vneshnikh istochnikov energovydeleniya”, Pisma v ZhTF, 14:8 (1988), 684–687

[17] Artemev V. I., Bergelson V. I., Nemchinov I. V. i dr., “Izmenenie rezhima sverkhzvukovogo obtekaniya prepyatstviya pri vozniknovenii pered nim tonkogo razrezhennogo kanala”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1989, no. 5, 146–151

[18] Georgievskii P. Yu., Levin V. A., “Nestatsionarnoe vzaimodeistvie sfery s atmosfernymi temperaturnymi neodnorodnostyami pri sverkhzvukovom obtekanii”, Izv. RAN. Mekhan. zhidkosti i gaza, 1993, no. 4, 174–183 | MR

[19] Kolesnichenko Yu. F., Brovkin V. G., Azarova O. A. et al., Microwave energy release regimes for drag reduction in supersonic flows, Paper AIAA-2002-0353, 1–13

[20] Azarova O. A., Grudnitskii V. G., Kolesnichenko Yu. F., “Statsionarnoe obtekanie tel sverkhzvukovym potokom gaza, soderzhaschim beskonechnyi tonkii razrezhennyi kanal”, Matem. modelirovanie, 18:1 (2006), 79–87 | MR | Zbl

[21] Kolesnichenko Yu. F., Azarova O. A., Brovkin V. G. et al., Basics in beamed MW energy deposition for flow/flight control, Paper AIAA-2004-0669, 1–14

[22] Georgievskii P. Y., Levin V. A., Transition to irregular regimes of supersonic flows over bodies initiated by energy deposition, Paper AIAA-2005-1047, 1–9

[23] Georgievskii P. Y., Levin V. A., Stability problem for front separation regions control realized by energy deposition, Paper AIAA-2006-402, 1–7

[24] Azarova O. A., Kolesnichenko Yu. F., “On details of flow structure during the interaction of an infinite rarefied channel with a cylinder shock layer”, Proc. 7th Internat. Workshop on Magnetoplasma Aerodynamics (Moscow, April 2007), Inst. High Temperatures RAS, M., 2007, 101–113

[25] Azarova O. A., Kolesnichenko Yu. F., Turbulent mixing via eddies generation in pulsating flow mode, Proc. West-East High Speed Flow Field Conf. (WEHSFF Conference), Moscow, November 19–22, 2007

[26] Meshkov E. E., “Neustoichivost granitsy razdela dvukh gazov, uskoryaemoi udarnoi volnoi”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1969, no. 5, 151–158

[27] Michalke A., “On spatially growing disturbances in an inviscid shear layer”, J. Fluid Mech., 23:3 (1965), 521–544 | DOI | MR

[28] Fridman A. M., “Predskazanie i otkrytie silneishikh gidrodinamicheskikh neustoichivostei, vyzvannykh skachkom skorosti: teoriya i eksperiment”, Uspekhi fiz. nauk, 178:3 (2008), 225–242 | DOI

[29] Antonov A. N., Elizarova T. G., Pavlov A. N., Chetverushkin B. N., “Matematicheskoe modelirovanie kolebatelnykh rezhimov pri obtekanii tela s igloi”, Matem. modelirovanie, 1:1 (1989), 13–23 | Zbl

[30] Feszly D., Badcock K., Richards B. E., “Driving mechanisms of high-speed unsteady spiked body flows. Part 1: Pulsation Mode”, AIAA Journal, 42:1 (2004), 106

[31] Azarova O. A., Yanitskii V. E., “Chislennoe issledovanie statisticheskikh kharakteristik pulsatsii plotnosti v potoke s udarnoi volnoi”, Zh. vychisl. matem. i matem. fiz., 38:10 (1998), 1751–1757 | MR | Zbl

[32] Azarova O. A., Kolesnichenko Yu. F., “Chislennoe modelirovanie vozdeistviya tonkogo razrezhennogo kanala na sverkhzvukovoe obtekanie tsilindricheskogo tela s polostyu slozhnoi formy”, Matem. modelirovanie, 20:4 (2008), 27–39 | Zbl