Computation of equations up to a prescribed accuracy with respect to singular terms and defect of differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 41 (2001) no. 10, pp. 1566-1582 Cet article a éte moissonné depuis la source Math-Net.Ru

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A. N. Minailos. Computation of equations up to a prescribed accuracy with respect to singular terms and defect of differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 41 (2001) no. 10, pp. 1566-1582. http://geodesic.mathdoc.fr/item/ZVMMF_2001_41_10_a9/

[1] Petukhov I. V., “O konturnykh ryadakh i ikh primenenii v integralnykh metodakh”, Zh. vychisl. matem. i matem. fiz., 1:2 (1961), 196–207

[2] Bakhvalov N. S., “K optimizatsii metodov resheniya kraevykh zadach pri nalichii pogranichnogo sloya”, Zh. vychisl. matem. i matem. fiz., 9:4 (1969), 841–869

[3] Bakhvalov N. S., “Ob avtomaticheskom konstruirovanii setki integrirovaniya pri reshenii kraevykh zadach s pogranichnym sloem”, Zh. vychisl. matem. i matem. fiz., 39:8 (1999), 1290–1295 | MR | Zbl

[4] Kopteva N. V., “O ravnomernoi skhodimosti po malomu parametru skhemy s tsentralnoi raznostyu na sguschayuschikhsya setkakh”, Zh. vychisl. matem. i matem. fiz., 39:10 (1999), 1662–1678 | MR | Zbl

[5] Shishkin G. I., Setochnye approksimatsii singulyarno vozmuschennykh ellipticheskikh i parabolicheskikh uravnenii, UrO RAN, Ekaterinburg, 1992

[6] Golovachev Yu. P., Chislennoe modelirovanie techenii vyazkogo gaza v udarnom sloe, Nauka, M., 1996 | Zbl

[7] Minailos A. N., “Tochnost chislennykh reshenii uravnenii Nave-Stoksa”, Zh. vychisl. matem. i matem. fiz., 38:7 (1998), 1220–1232 | MR | Zbl

[8] Belotserkovskii O. M., “Matematicheskoe modelirovanie na superkompyuterakh (opyt i tendentsii)”, Zh. vychisl. matem. i matem. fiz., 40:8 (2000), 1221–1236

[9] Godunov C. K., Ryabenkii B. C., Raznostnye skhemy, Nauka, M., 1977

[10] Shlikhting G., Teoriya pogranichnogo sloya, Nauka, M., 1974

[11] Kopchenov V. I., Kraiko A. N., Levin M. P., “K ispolzovaniyu suschestvenno neravnomernykh setok pri chislennom reshenii uravnenii Nave-Stoksa”, Zh. vychisl. matem. i matem. fiz., 22:6 (1982), 1457–1467 | MR

[12] Landahl M. T., “CFD and turbulence”, 17$^{\mathrm{th}}$ ICAS Congress, ICAS-90-0.1, 1990, XXX–XXXIX

[13] Marvin J. G., “Turbulence modeling for hypersonic flow”, 3d Joint Europe, US Short Course in Hypersonics, RWTH, Aachen, 1990

[14] Belotserkovskii O. M. (red.), Etyudy o turbulentnosti, Nauka, M., 1994

[15] Luschik V. G., Pavelev A. A., Yakubenko A. E., “Turbulentnye techeniya. Modeli i chislennye issledovaniya”, obzor, Izv. RAN. Mekhan. zhidkosti i gaza, 1994, no. 4, 4–27 | MR

[16] Cheng Sin-I., “Accuracy of difference formulation of Navier-Stokes equations”, Phys. Fluids, 12:2, Supple (1969), 34–41 | DOI | Zbl

[17] Castro I. P., “Numerical difficalties in the calculation of complex turbulent flows”, Turbulent Shear Flows, 1980, 220–236

[18] Richardson L. F., “Atmosheric diffusion shown on a distance-neighbour graph”, Proc. Roy. Soc. London A, 110:756 (1926), 709–737 | DOI

[19] Onzager L., “The distribution of energy in turbulence”, Phys. Rev., 68:11–12 (1945), 286

[20] Kuznetsov V. P., Praskovskii A. A., Sabelnikov V. A., “Gipoteza o statisticheskoi nezavisimosti melko- i krupnomasshtabnogo dvizhenii v teorii turbulentnosti”, Etyudy o turbulentnosti, Nauka, M., 1994

[21] Helliwell W. S., Alber I. E., Dickinson R. P., Lubard S. C., Turbulent flow over vehicles at angle of attack, AIAA Paper No 82-0027, 1982, 12 pp.

[22] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Nauka, M., 1987 | MR

[23] Landau L. D., Lifshits E. M., Mekhanika sploshnykh sred, Gostekhteorizdat, M., 1954

[24] Klimontovich Yu. L., Turbulentnoe dvizhenie i struktura khaosa. Novyi podkhod k statisticheskoi teorii otkrytykh sistem, Nauka, M., 1990 | MR

[25] Vinogradova M. B., Rudenko O. V., Sukhorukov A. P., Teoriya voln, Nauka, M., 1990 | MR | Zbl

[26] Karamzin Yu. N., Sukhorukov A. P., Trofimov V. A., Matematicheskoe modelirovanie v nelineinoi optike, Izd-vo MGU, M., 1989 | MR | Zbl

[27] Sukhorukov A. P., Nelineinye volnovye vzaimodeistviya v optike i radiofizike, Nauka, M., 1988

[28] Krylov A. N., Lektsii o priblizhennykh vychisleniyakh, Gostekhteorizdat, M.–L., 1950

[29] McNeil C. Y., The effect of numerical dissipation on high Reynolds number turbulent flow solutions, AIAA Paper No 96-0891, 1996, 11 pp. | Zbl

[30] Krupa V. G., “O postroenii raznostnykh skhem povyshennoi tochnosti dlya giperbolicheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz., 38:1 (1998), 85–98 | MR | Zbl

[31] Tolstykh A. I., Kompaktnye raznostnye skhemy i ikh primenenie v zadachakh aerogidrodinamiki, Nauka, M., 1990 | MR

[32] Pinchukov V. I., “Kompaktnaya skhema shestogo poryadka dlya resheniya uravnenii Eilera”, Zh. vychisl. matem. i matem. fiz., 38:10 (1998), 1717–1720 | MR | Zbl

[33] Pinchukov V. I., “Korrektsiya potokov v mnogomernykh zadachakh giperbolicheskogo i parabolicheskogo tipa”, Zh. vychisl. matem. i matem. fiz., 36:4 (1996), 26–40 | MR | Zbl

[34] Minailos A. N., “O korrektnoi postanovke zadach chislennogo resheniya uravnenii Nave-Stoksa pri bolshikh chislakh Reinoldsa”, Fundamentalnye issledovaniya dlya giperzvukovykh tekhnologii, Vseros. nauchno-tekhn. konf. (g. Zhukovskii, 20–23.10.1998 g.), TsAGI, Zhukovskii, 487–494

[35] Betchelor Dzh., Vvedenie v dinamiku zhidkosti, Mir, M., 1973

[36] Severinov L. I., “O primenenii zakonov izmeneniya kolichestvennykh mer dvizheniya dlya konechnogo ob'ema v konechnykh prirascheniyakh pri chislennom reshenii zadach mekhaniki sploshnoi sredy”, Probl. aksiomatiki v razvitii protsessov, 1, Sistem-prognoz, M., 1993, 66–95

[37] Garanzha V. A., Tolstykh A. I., “O chislennom modelirovanii nestatsionarnykh otryvnykh techenii neszhimaemoi zhidkosti na osnove kompaktnykh approksimatsii pyatogo poryadka”, Dokl. AN SSSR, 312:2 (1990), 311–314 | Zbl

[38] Tolstykh A. I., Shirobokov D. A., “O raznostnykh skhemakh s kompaktnymi approksimatsiyami pyatogo poryadka dlya prostranstvennykh techenii gaza”, Zh. vychisl. matem. i matem. fiz., 36:4 (1996), 71–85 | MR | Zbl

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

[40] Liseikin V. D., “Metod algebraicheskoi adaptatsii”, Zh. vychisl. matem. i matem. fiz., 38:10 (1998), 1692–1709 | MR | Zbl

[41] Moretti G., “A technique for integrating two-dimensional Euler equations”, Comput. and Fluids, 15 (1987), 59–75 | DOI | MR | Zbl

[42] Kalitkin N. N., Shlyakhov H. M., “$\mathrm{B}$-splainy vysokikh stepenei”, Matem. modelirovanie, 11:11 (1999), 64–74 | MR | Zbl

[43] Yamamoto Y., Karashima K., “Floating shock fitting for three-dimensional inviscid supersonic flows”, AIAA Journal, 20:1 (1982), 9–17 | DOI | Zbl

[44] Minailos A. N., “O znachenii monotonnosti konechno-raznostnykh skhem v metodakh skvoznogo scheta”, Zh. vychisl. matem. i matem. fiz., 17:4 (1977), 1058–1063

[45] Kolgan V. P., “Primenenie printsipa minimalnykh znachenii proizvodnoi k postroeniyu konechno-raznostnykh skhem dlya rascheta razryvnykh reshenii gazovoi dinamiki”, Uch. zap. TsAGI, 3:6 (1972), 68–77