The use of high-order composite compact schemes for computing supersonic jet interaction with a surface

A. D. Savel'ev

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 10, pp. 1746-1759

Résumé

High-order composite compact schemes are applied to the simulation of viscous gas dynamics with strong discontinuities of flow variables. To perform shock-capturing computations of such problems, the dissipation of the basic operators is enhanced and the solutions obtained with these operators are locally replaced by those produced with the help of simple one-sided differences. Numerical results obtained for the shock interaction of a supersonic axisymmetric jet with a flat surface are presented.

Bibliographie

[1] Tolstykh A. I., “Multioperatornye skhemy proizvolnogo poryadka, ispolzuyuschie netsentrirovannye kompaktnye approksimatsii”, Dokl. AN, 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] Lele S., Lele S. K., Moin P., “Direct numerical simulation of isotropic turbulence interacting with a shock wave”, J. Fluid Mech., 251 (1993), 533–562 | DOI

[6] Bogey C., d'Cacqueray N., Bailly C., “A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations”, J. Comput. Phys., 228 (2009), 1447–1465 | DOI | MR | Zbl

[7] 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

[8] Mikhailovskaya M. N., Rogov B. V., “Monotonnye kompaktnye skhemy beguschego scheta dlya sistem uravnenii giperbolicheskogo tipa”, Zh. vychisl. matem. i matem. fiz., 52:4 (2012), 672–695 | MR

[9] Tolstykh A. I., “O gibridnykh skhemakh s multioperatorami vysokogo poryadka dlya scheta razryvnykh reshenii”, Zh. vychisl. matem. i matem. fiz., 53:9 (2013), 1481–1502 | DOI

[10] Bradshow P., Edna M. L., The normal impingement of a circular air jet on a flat surface, Reports and Memoranda No 3205, Aerodynamical Division, N.P.L., September, 1959

[11] Donaldson C. D., Snedeker R. S., “A study of free jet impingement. 1: Mean properties of free and impinging jets”, J. Fluid Mech., 45 (1971), 281–319 | DOI

[12] Ginzberg I. P., Semilentenko B. G., Terpigorev V. S., Uskov V. N., “Some singularities of supersonic underexpanded jet interaction with a plane obstacle”, J. Eng. Phys., 19 (1973), 1081–1084 | DOI

[13] Lamont P. J., Hunt B. L., “The impingement of underexpanded axisymmetric jets on perpendicular and inclined flat plates”, J. Fluid Mech., 100 (1980), 471–511 | DOI

[14] Krothapalli A., “Discrete tones generated by an impinging underexpanded rectangular jet”, AIAA J., 23 (1985), 1910–1915 | DOI

[15] Kuo C., Dowling A. P., “Oscillations of a moderately underexpanded choked jet impinging upon a flat plates”, J. Fluid Mech., 315 (1996), 267–291 | DOI | Zbl

[16] Krothapalli A., Rajakuperan E., Alvi F. S., Lourenco L., “Flow field and noise characteristics of supersonic impinging jet”, J. Fluid Mech., 392 (1999), 155–181 | DOI | Zbl

[17] Henderson B., Bridges J., Wernet M., “An experimental study of the oscillatory flow structure of tone-producing supersonic impinging jets”, J. Fluid Mech., 542 (2005), 115–137 | DOI | Zbl

[18] Dubinskaya N. V., Ivanov M. Ya., “K raschetu vzaimodeistviya sverkhzvukovoi strui idealnogo gaza s ploskoi pregradoi, perpendikulyarnoi ee osi”, Uch. zap. TsAGI, 6:5 (1975), 38–44

[19] Godunov S. K., Zabrodin A. V., Ivanov M. Ya., Kraiko A. N. i dr., Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki, Nauka, M., 1976 | MR | Zbl

[20] Sakakibara Y., Iwamoto J., “Numerical study of oscillation mechanism in underexpanded jet impinging on plate”, J. Fluids Eng., 120 (1998), 477 | DOI

[21] Gribben B. J., Badcock K. J., Richards B. E., “Numerical study of shock-reflection hysteresis in an underexpanded jet”, AIAA J., 38 (2000), 275–283 | DOI

[22] Kim S. I., Park S. O., “Numerical analysis of the oscillatory behaviors of supersonic impinging jet flow”, 24th Int. Cong. Aeron. Sci. (2004)

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

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

[25] Savelev A. D., “Prakticheskoe sravnenie dvukh turbulentnykh modelei”, Matem. modelir., 21:9 (2009), 108–120

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

[27] Savelev A. D., “Sostavnye kompaktnye skhemy vysokogo poryadka dlya modelirovaniya techenii vyazkogo gaza”, Zh. vychisl. matem. i matem. fiz., 47:8 (2007), 1387–1401 | MR

[28] Savelev A. D., “Primenenie raznostnykh operatorov vysokogo poryadka pri chislennom modelirovanii zadach aerodinamiki”, Matem. modelirovanie, 24:4 (2012), 80–94 | MR

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