Geodesic
High-order composite compact schemes for simulation of viscous gas flows
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 8, pp. 1387-1401 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Differential schemes up to the seventh order are used for a numerical description of conservation laws on curvilinear grids. The schemes combine symmetric compact differences and diffusiontype operators oriented according to the direction of characteristics. The spectral properties of the schemes are examined. Several model problems are computed. A numerical method for the Navier–Stokes equations combined with a two-parameter turbulence model is used to simulate two-dimensional viscous gas flows. 
@article{ZVMMF_2007_47_8_a10,
     author = {A. D. Savel'ev},
     title = {High-order composite compact schemes for simulation of viscous gas flows},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1387--1401},
     year = {2007},
     volume = {47},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_8_a10/}
}
TY  - JOUR
AU  - A. D. Savel'ev
TI  - High-order composite compact schemes for simulation of viscous gas flows
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2007
SP  - 1387
EP  - 1401
VL  - 47
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_8_a10/
LA  - ru
ID  - ZVMMF_2007_47_8_a10
ER  - 
%0 Journal Article
%A A. D. Savel'ev
%T High-order composite compact schemes for simulation of viscous gas flows
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2007
%P 1387-1401
%V 47
%N 8
%U http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_8_a10/
%G ru
%F ZVMMF_2007_47_8_a10
A. D. Savel'ev. High-order composite compact schemes for simulation of viscous gas flows. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 8, pp. 1387-1401. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_8_a10/

[1] Tolstykh A. I., “O metode chislennogo resheniya uravnenii Nave–Stoksa szhimaemogo gaza v shirokom diapazone chisel Reinoldsa”, Dokl. AN SSSR, 210:1 (1973), 48–51

[2] Tele S. K., “Compact finite difference schemes with spectral-like resolution”, J. Comput. Phys., 102 (1992), 16–42 | MR

[3] Lele S., Lele S. K., Moin P., “Direct numerical simulation of isotropic turbylence interacting with a shock wave”, J. Fluid. Mech., 251 (1993), 533–562 | DOI

[4] Visbai M. R., Gaitonde D. V., “On the use of high-order finite-difference shcemes on curvilinear and deforming meshes”, J. Comput. Phys., 181 (2002), 155–185 | DOI | MR

[5] Tolstykh A. I., High accuracy non-centered compact schemes for fluid dynamics applicatins, World Sci., Singapore, 1994 | Zbl

[6] Tolstykh A. I., “Multioperatornye skhemy proizvolnogo poryadka, ispolzuyuschie netsentrirovannye kompaktnye approksimatsii”, Dokl. RAN, 366:3 (1999), 319–322 | MR | Zbl

[7] Garanzha V. A., Konshin V. N., “Chislennye algoritmy dlya techenii vyazkoi zhidkosti, osnovannye na konservativnykh kompaktnykh skhemakh vysokogo poryadka approksimatsii”, Zh. vychisl. matem. i matem. fiz., 39:8 (1999), 1378–1392 | MR | Zbl

[8] Pulliam T. H., “Arfiticial dissipation models for the Euler equations”, AIAA. Journal, 24:12 (1986), 1931–1940 | DOI | Zbl

[9] Savelev A. D., O raznostnykh skhemakh vysokogo poryadka s sostavnymi stabiliziruyuschimi dobavkami, VTs RAN, M., 2003

[10] Chareravathv S. R., Osker S., A new class of high accuracy TVD schemes for hyperbolic consservation laws, AIAA Paper No 85-0363, 1985, 11 pp.

[11] Cockburn B., Shu C. W., “Nonlinearly stable compact schemes for shock calculations”, SIAM J. Numer. Analys., 31:3 (1994), 607–627 | DOI | MR | Zbl

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

[13] Savelev A. D., “Raschety techenii vyazkogo gaza na osnove $(q-\nu)$-modeli turbulentnosti”, Zh. vychisl. matem. i matem. fiz., 43:4 (2003), 589–600 | MR

[14] Steger Zh. L., “Neyavnyi konechno-raznostnyi metod dlya rascheta dvumernogo techeniya okolo tel proizvolnoi formy”, Raketnaya tekhn. i kosmonavtika, 16:7 (1978), 51–60

[15] Steger J. L., Warming R. F., “Flux vector spliting in the inviscid gas dynamic equations with applications to finite difference methods”, J. Comput. Phys., 40 (1981), 263–293 | DOI | MR | Zbl

[16] Yee H. C., Sandham N. D., Djomehri M. J., “Low dissipation high order shock-capturing methods usinc characteristic-based filters”, J. Comput. Phys., 150 (1999), 199–238 | DOI | MR | Zbl

[17] Lipavskii M. V., Tolstykh A. I., “O sravnitelnoi effektivnosti skhem s netsentrirovannymi kompaktnymi approksimatsiyami”, Zh. vychisl. matem. i matem. fiz., 39:10 (1999), 1705–1720 | MR

[18] Setls Zh. S., Ves M. E., Bogdonov S. M., “Podrobnaya struktura turbulentnogo pogranichnogo sloya, otorvavshegosya pod deistviem skachka uplotneniya pered uglom szhatiya”, Raketnaya tekhn. i kosmonavtika, 14:12 (1976), 55–63

[19] Holst T. J., Viscous transonic airfoil workshop. Compendium of results, AIAA Paper No 87-1460, 1987, 32 pp.

[20] Coacley T. J., Turbulence modeling method for the compressible Navier–Stokes equations, AIAA Paper No 83-1693, 1983, 9 pp.

[21] Johnson D. A., King L. S., “A mathematically simple turbulence closure model for attached and separated boundary layers”, AIAA Journal, 23:11 (1985), 1684–1692 | DOI | MR