Geodesic
Localization of singularities in gas-dynamic fields with the aid of wavelet analyses
Matematičeskoe modelirovanie, Tome 20 (2008) no. 7, pp. 65-84 
A. L. Afendikov; L. I. Levkovich-Maslyuk; A. E. Lutsky; A. V. Plenkin. Localization of singularities in gas-dynamic fields with the aid of wavelet analyses. Matematičeskoe modelirovanie, Tome 20 (2008) no. 7, pp. 65-84. http://geodesic.mathdoc.fr/item/MM_2008_20_7_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The article is devoted to construction of an algorithm for detection and classification of singularities of the gas dynamics fields obtained by numerical modeling. The algorithm employs wavelet expansions of the gas dynamics fields, with subsequent analysis of the obtained coefficients. The ideas of the approach originate from [1, 2, 3]. In the current article we suggest a detection and classification algorithm of linear computational complexity. It employs expansion of the gas-dynamic field components in the basis of symmetric complex-valued orthogonal wavelets, and post-processing with the aid of classical real-valued Daubechies wavelets. Algorithm was used for analysis of two-dimensional gas flow structure in the process of controlling the flow by local energy release.

[1] A. L. Afendikov, V. V. Gorbunova, L. I. Levkovich-Maslyuk, A. V. Plenkin, Lokalizatsiya singulyarnostei gazodinamicheskikh polei pri pomoschi kompleksnykh i veschestvennykh veivletov, preprint No 98, IPM im. M. V. Keldysha RAN, M., 2005

[2] A. L. Afendikov, L. I. Levkovich-Maslyuk, Lokalizatsiya osobennostei gazodinamicheskikh polei pri pomoschi kompleksnykh ortogonalnykh veivlet-razlozhenii, preprint No 101, IPM im. M. V. Keldysha RAN, M., 2003

[3] A. Afendikov, L. Levkovich-Masliuk, “Localization of Singularities of Gas-Dynamic fields by using complex orthogonal wavelet expansion”, Russian Journal of Math. Phys., 7:3 (2004), 250–258 | MR

[4] E. V. Vorozhtsov, N. N. Yanenko, Metody lokalizatsii osobennostei v vychislitelnoi gazodinamike, Nauka, Novosibirsk, 1985 | Zbl

[5] S. Bazarov, “Primenenie metodov obrabotki izobrazhenii v vychislitelnoi gazodinamike”, Trudy GraphiCon, 98, M., 1998, 258–264

[6] J.-M. Lina, Daubechies wavelets: filters design and applications, CRM-2449, ISAAC Conference, University of Delaware, 1997 | Zbl

[7] I. Dobeshi, Desyat lektsii po veivletam, NITs “Regulyarnaya i khaoticheskaya dinamika”, Moskva–Izhevsk, 2004

[8] W. Lawton, “Application of complex valued wavelet transform to subband decomposition”, IEEE Transition Signal Processing, 41:12 (1993), 3566–3568 | DOI | Zbl

[9] Stefan Mala, Veivlety v obrabotke signalov, Mir, M., 2005

[10] I. A. Znamenskaya, A. E. Lutskii, Issledovanie evolyutsii i vzaimodeistviya razryvov techeniya v kanale pod deistviem impulsnogo vlozheniya energii, preprint No 88, IPM im. M. V. Keldysha RAN, 2005

[11] I. A. Znamenskaya, A. E. Lutskii, I. V. Mursenkova, “Issledovanie poverkhnostnogo energovklada v gaz pri initsiirovanii impulsnogo razryada tipa “plazmennyi list””, Pisma v ZhETF, 30:24 (2004), 38–42