Geodesic
Complex conservative difference schemes for computing supersonic flows past simple aerodynamic forms
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2067-2092 Cet article a éte moissonné depuis la source Math-Net.Ru

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Complex conservative modifications of two-dimensional difference schemes on a minimum stencil are presented for the Euler equations. The schemes are conservative with respect to the basic divergent variables and the divergent variables for spatial derivatives. Approximations of boundary conditions for computing flows around variously shaped bodies (plates, cylinders, wedges, cones, bodies with cavities, and compound bodies) are constructed without violating the conservation properties in the computational domain. Test problems for computing flows with shock waves and contact discontinuities and supersonic flows with external energy sources are described. 
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O. A. Azarova. Complex conservative difference schemes for computing supersonic flows past simple aerodynamic forms. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2067-2092. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a9/

[1] Lax P. D., “Weak solutions of nonlinear hyperbolic equations and their numerical computation”, Comm. Pure and Appl. Math., 7 (1954), 159–193 | DOI | MR | Zbl

[2] Lax P. D., “Hyperbolic system of conservation laws, II”, Comm. Pure and Appl. Math., 10:4 (1957), 537–566 | DOI | MR | Zbl

[3] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1977, 656 pp. | MR

[4] Godunov S. K., Romenskii E. I., Elementy mekhaniki sploshnykh sred i zakony sokhraneniya, Nauchn. kniga, Novosibirsk, 1998, 280 pp.

[5] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1977, 335 pp.

[6] Samarskii A. A., Popov Yu. P., Raznostnye metody resheniya zadach gazovoi dinamiki, Nauka, M., 1992, 424 pp. | MR

[7] Rouch P., Vychislitelnaya gidrodinamika, Mir, M., 1980, 616 pp.

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

[9] Godunov S. K., “Problema obobschennogo resheniya v teorii kvazilineinykh uravnenii i v gazovoi dinamike”, Uspekhi matem. nauk, 17:3(105) (1962), 147–158 | MR | Zbl

[10] S. K. Godunov (red.), Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki, Nauka, M., 1976, 400 pp. | MR

[11] Part-Enander E., Sjogreen B., “Conservative and non-conservative interpolation between overlapping grids for finite volume solutions of hyperbolic problems”, Computer fluids, 23 (1994), 551–574 | DOI | MR | Zbl

[12] Li S., WENO Schemes for cylindrical and spherical geometry, Los Alamos Report LA-UR-03-8922, Theoretical Division, MS B284, Los Alamos National Laboratory, Los Alamos, NM 87545, Oct. 2003, 14 pp.

[13] 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 | Zbl

[14] 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 | Zbl

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

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

[17] 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

[18] Tusheva A. A., Shokin Yu. N., Yanenko N. N., “O postroenii raznostnykh skhem povyshennogo poryadka approksimatsii na osnove differentsialnykh sledstvii”, Nekotorye probl. vychisl. i prikl. matem., Nauka, Novosibirsk, 1975, 184–191

[19] Yabe T., Aoki T., Sakaguchi G., Wang P.-Y., Ishikawa T., “The compact CIP (cubic-interpolated pseudo-particle) method as a general hyperbolic solver”, Computers Fluids, 19:3–4 (1991), 421–431 | DOI | MR | Zbl

[20] Chang S. C., “The method of space-time conservation element and solution element — a new approach for solving the Navier-Stokes and Euler equations”, J. Comput. Phys., 119:2 (1995), 295–324 | DOI | MR | Zbl

[21] 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

[22] Tolstykh A. I., “Development of arbitrary-order multioperators-based schemes for parallel calculations. 1: Higherthan-fifth order approximations to convection terms”, J. Comput. Phys., 225:2 (2007), 2333–2353 | DOI | MR | Zbl

[23] Tolstykh A. I., “Development of arbitrary-order multioperators-based schemes for parallel calculations. Part 2: Families of compact approximations with two-diagonal inversions and related multioperators”, J. Comput. Phys., 227 (2008), 2922–2940 | DOI | MR | Zbl

[24] Lipavskii M. V., Tolstykh A. I., Chigerev E. N., “O skheme s multioperatornymi approksimatsiyami 9-go poryadka dlya parallelnykh vychislenii ioe e primenenii v zadachakh pryamogo chislennogo modelirovaniya”, Zh. vychisl. matem. i matem. fiz., 46:8 (2006), 1433–1452 | MR

[25] Popov Yu. P., Samarskii A. A., “Polnostyu konservativnye raznostnye skhemy”, Zh. vychisl. matem. i matem. fiz., 9:4 (1969), 953–958 | MR | Zbl

[26] Ryazanov M. A., Polnostyu konservativnye raznostnye skhemy gazovoi dinamiki v eilerovykh peremennykh, Diss. kand. fiz.-matem. nauk, MGU. VMK, M., 1984, 179 pp.

[27] Azarova O. A., “Ob odnoi raznostnoi skheme na minimalnom shablone dlya rascheta dvumernykh osesimmetrichnykh techenii gaza. Primery pulsiruyuschikh potokov s neustoichivostyami”, Zh. vychisl. matem. i matem. fiz., 49:4 (2009), 734–753 | MR | Zbl

[28] Azarova O. A., “Complex conservative difference schemes in modelling instabilities and contact structures”, 28th Int. Symposium on Shock Waves (Manchester, UK, 17–22 July, 2011), v. 2, ed. K. Kontis, Springer, 2012, 683–689 | DOI

[29] Grudnitskii V. G., “O povedenii chislennogo resheniya kraevykh zadach dlya evolyutsionnykh uravnenii v bolshikh oblastyakh”, Dokl. AN SSSR, 252:5 (1980), 1041–1044 | MR | Zbl

[30] 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

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

[32] Azarova O. A., Knight D., Kolesnichenko Yu. F., “Flowfields around supersonic aerodynamic bodies under the action of asymmetric energy release”, Progress in Flight Physics, EDP Sciences, 5, 2013, 139–152

[33] Mortazavi M., Knight D., Azarova O., Shix J., Yan H., Numerical simulation of energy deposition in a supersonic flow past a hemisphere, Paper AIAA-2014-0944, 18 pp.

[34] Uizem Dzh., Lineinye i nelineinye volny, Mir, M., 1977, 724 pp. | MR

[35] V. M. Borisov (red.), Algoritmy dlya chislennogo issledovaniya razryvnykh techenii, VTs RAN, M., 1993, 204 pp.

[36] Artemev V. I., Bergelson V. I., Nemchinov I. V., Orlova T. I., Smirnov V. A., Khazins V. M., “Izmenenie rezhima sverkhzvukovogo obtekaniya prepyatstviya pri vozniknovenii pered nim tonkogo razrezhennogo kanala”, Mekhan. zhidkosti i gaza, 1989, no. 5, 146–151

[37] Azarova O. A., Knight D., Kolesnichenko Yu. F., “Pulsating stochastic flows accompanying microwave filament/supersonic shock layer interaction”, Shock Waves, 21:5 (2011), 439–450 | DOI

[38] Hirshel E., Basics on aerothermodynamics, Springer, New York, 2005, 427 pp.

[39] Azarova O. A., “Modelirovanie stokhasticheskikh pulsatsionnykh techenii s neustoichivostyami na osnove raznostnykh skhem na minimalnom shablone”, Zh. vychisl. matem. i matem. fiz., 49:8 (2009), 1466–1483 | MR | Zbl

[40] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii, Nauka, M., 1968, 687 pp.

[41] Azarova O. A., “Supersonic flow control using combined energy deposition”, Aerospace, 2:1 (2015), 118–134 | DOI

[42] Azarova O. A., “Generation of Richtmyer–Meshkov and secondary instabilities during the interaction of an energy release with a cylinder shock layer”, Aerospace Science and Technology, 42 (2015), 376–383 | DOI

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