Geodesic
Application of high-order accuracy schemes to numerical simulation of unsteady supersonic flows
Matematičeskoe modelirovanie, Tome 19 (2007) no. 7, pp. 39-55 
A. N. Kudryavtsev; T. V. Poplavskaya; D. V. Khotyanovsky. Application of high-order accuracy schemes to numerical simulation of unsteady supersonic flows. Matematičeskoe modelirovanie, Tome 19 (2007) no. 7, pp. 39-55. http://geodesic.mathdoc.fr/item/MM_2007_19_7_a3/
@article{MM_2007_19_7_a3,
     author = {A. N. Kudryavtsev and T. V. Poplavskaya and D. V. Khotyanovsky},
     title = {Application of high-order accuracy schemes to numerical simulation of unsteady supersonic flows},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {39--55},
     year = {2007},
     volume = {19},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2007_19_7_a3/}
}
TY  - JOUR
AU  - A. N. Kudryavtsev
AU  - T. V. Poplavskaya
AU  - D. V. Khotyanovsky
TI  - Application of high-order accuracy schemes to numerical simulation of unsteady supersonic flows
JO  - Matematičeskoe modelirovanie
PY  - 2007
SP  - 39
EP  - 55
VL  - 19
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/MM_2007_19_7_a3/
LA  - ru
ID  - MM_2007_19_7_a3
ER  - 
%0 Journal Article
%A A. N. Kudryavtsev
%A T. V. Poplavskaya
%A D. V. Khotyanovsky
%T Application of high-order accuracy schemes to numerical simulation of unsteady supersonic flows
%J Matematičeskoe modelirovanie
%D 2007
%P 39-55
%V 19
%N 7
%U http://geodesic.mathdoc.fr/item/MM_2007_19_7_a3/
%G ru
%F MM_2007_19_7_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

Employment of high-order shock-capturing methods for numerical simulation of complex supersonic flows is considered. The procedure of construction of WENO (weighted essentially non-oscillatory) schemes and their basic properties are briefly reviewed. The problems arising at their practical implementation for solving the Euler and Navier–Stokes equations are discussed. A number of examples of solving the problems of computational aerodynamics are given. In many cases, results obtained from numerical simulations are compared with data of experimental measurements.

[1] Canuto C., Hussaini M. Y., Quarteroni A., Zang T. A., Spectral Methods in Fluid Dynamics, Springer-Verlag, New York, 1988 | MR

[2] Lele S. K., “Compact finite-difference schemes with spectral-like resolution”, J. Comput. Phys., 103 (1992), 16–42 | DOI | MR | Zbl

[3] Moin K., Mahesh K., “Direct Numerical Simulation: A tool in turbulence research”, Ann. Rev. Fluid Mech., 30 (1998), 539–578 | DOI | MR

[4] Sagault P., Large Eddy Simulation for Incompressible Flows. An Introduction., Springer, Heidelberg, 2001 | MR

[5] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskie voprosy resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001 | Zbl

[6] Jiang G.-S., Shu C.-W., “Efficient implementation of weighted ENO schemes”, J. Comput. Phys., 126 (1996), 202–228 | DOI | MR | Zbl

[7] Shu C.-W., “High order ENO and WENO schemes for computational fluid dynamics”, High-Order Methods for Computational Physics, Lecture Notes in Computational Science and Engineering, 9, eds. T. J. Barth, H. Deconinck, Springer, 1999, 439–582 | MR | Zbl

[8] Shu C.-W., Osher S., “Efficient implementation of essentially non-oscillatory shock capturing schemes”, J. Comput. Phys., 77 (1988), 439–471 | DOI | MR | Zbl

[9] Khairer E., Nersett S., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Nezhestkie zadachi, Mir, M., 1990 | MR

[10] Casper J., Shu C.-W., Atkiins H., “Comparison of two formulations for high-order accurate essentially non-oscilatory schemes”, AIAA Journal, 32 (1994), 1970–1977 | DOI | Zbl

[11] LeVeque R. J., Numerical Methods for Conservation Laws, Birkhauser, Basel, 1992 | MR | Zbl

[12] Ivanov M. Ya., Kraiko A. N., “Ob approksimatsii razryvnykh reshenii pri ispolzovanii raznostnykh skhem skvoznogo scheta”, ZhVMiMF, 18 (1978), 780–783

[13] Ostapenko V. V., “O skhodimosti raznostnykh skhem za frontom nestatsionarnoi udarnoi volny”, ZhVMiMF, 37 (1997), 1201–1212 | MR | Zbl

[14] Roberts T. W., “The behavior of flux difference splitting schemes near slowly moving shock waves”, J. Comput. Phys., 90 (1990), 141–160 | DOI | MR | Zbl

[15] Yates L. A., “Images constructed from computed flowfields”, AIAA Journal, 31 (1993), 1877–1884 | DOI

[16] Schardin H., “High frequency cinematography in the shock tube”, Journal of Photographic Science, 5 (1957), 19–26

[17] Van Daik M., Albom techenii zhidkosti i gaza, Mir, M., 1986

[18] Amann H. O., “Experimental study of the starting process in a reflection nozzle”, Phys. Fluids, 12 (1969), 150–153 | DOI

[19] Jiang Z., Onodera O., Takayama K., “Evolution of shock waves and the primary vortex loop discharged from a square cross-sectional tube”, Shock Waves, 9 (1990), 1–10 | DOI

[20] Mironov S. G., Maslov A. A., “An experimental study of density waves in a hypersonic shock layer on a flat plate”, Phys. Fluids, 12 (2000), 1544–1553 | DOI | Zbl

[21] Kogan M. N., Dinamika razrezhennogo gaza, Nauka, M., 1967

[22] Grinstein F., Fureby C., “Recent progress on MILES for high Reynolds number flows”, J. Fluids Eng., 124 (2002), 848–861 | DOI