Geodesic
Applications of high order differenses in aerodynamical simulations
Matematičeskoe modelirovanie, Tome 24 (2012) no. 4, pp. 80-94.

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The differential schemes based on symmetrical compact differences of 6th and 8th order of accuracy and characteristically directed diffusing operators are considered. Their spectral properties are analyzed and possibility of improvement of dissipative characteristics is investigated. For the description of viscous members of equations the differences of a high order also are used. Some problems of compressible gas, including a non-stationary flow of a symmetric aerodynamic profile in a subsonic laminar stream are considered.
Keywords: numerical simulation, high-accuracy compact schemes, Navier–Stokes equations, laminar and turbulent viscous gas flows
Mots-clés : acoustic noise of airfoil. 
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A. D. Savel'ev. Applications of high order differenses in aerodynamical simulations. Matematičeskoe modelirovanie, Tome 24 (2012) no. 4, pp. 80-94. http://geodesic.mathdoc.fr/item/MM_2012_24_4_a5/

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

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

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

[4] Bogey C., Bailly C., “A family of low dispersive and low dissipative explicit schemes for noise computations”, J. Comput. Phys., 194 (2004), 194–214 | DOI | Zbl

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

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

[7] Menter F. R., Zonal two equation k-$\omega$ turbulence models for aerodynamic flows, AIAA Paper 93-2906, 1993, 21 pp.

[8] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Nauka, M., 1987, 840 pp. | MR

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

[10] A. D. Savelev, “Sostavnye kompaktnye skhemy vysokogo poryadka dlya modelirovaniya techenii vyazkogo gaza”, Zh. vychisl.matem. i matem. fiz., 47:8 (2007), 1389–1403 | MR

[11] Pulliam T. H., “Artificial dissipation models for the Euler equations”, AIAA Journal, 24:12, 1931–1940 | Zbl

[12] Lipavskii M. V., Tolstykh A. I., “Multioperatornye kompaktnye skhemy 5-go i 7-go poryadkov”, Zh. vychisl. matem. i matem. fiz., 43:7 (2003), 1018–1034 | MR | Zbl

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

[14] Savelev A. D., “O strukture vnutrennei dissipatsii sostavnykh kompaktnykh skhem dlya resheniya zadach vychislitelnoi gazovoi dinamiki”, Zh. vychisl. matem. i matem. fiz., 49:12 (2009), 2232–2246 | MR

[15] Amiet R. K., “Noise due to turbulent flow past a trailing edge”, J. of sound and vibration, 47:3 (1976), 387–393 | DOI

[16] Marsden O., Bogey C., Bailly C., “High-order curvilinear simulations of flows around non-cartesian bodies”, J. of comput. acoustics, 13:4 (2005), 731–748 | DOI | Zbl