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Matem. Mod., 2008, Volume 20, Number 7, Pages 65–84 (Mi mm2695)  

This article is cited in 10 scientific papers (total in 10 papers)

Localization of singularities in gas-dynamic fields with the aid of wavelet analyses

A. L. Afendikov, L. I. Levkovich-Maslyuk, A. E. Lutsky, A. V. Plenkin

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: 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.

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English version:
Mathematical Models and Computer Simulations, 2009, 1:4, 453–469

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Received: 07.11.2006
Revised: 22.11.2007

Citation: 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”, Matem. Mod., 20:7 (2008), 65–84; Math. Models Comput. Simul., 1:4 (2009), 453–469

Citation in format AMSBIB
\by A.~L.~Afendikov, L.~I.~Levkovich-Maslyuk, A.~E.~Lutsky, A.~V.~Plenkin
\paper Localization of singularities in gas-dynamic fields with the aid of wavelet analyses
\jour Matem. Mod.
\yr 2008
\vol 20
\issue 7
\pages 65--84
\jour Math. Models Comput. Simul.
\yr 2009
\vol 1
\issue 4
\pages 453--469

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    This publication is cited in the following articles:
    1. A. L. Afendikov, A. E. Lutskii, A. V. Plenkin, “Mnogomasshtabnyi analiz osobennostei gazodinamicheskikh polei”, Preprinty IPM im. M. V. Keldysha, 2008, 098, 17 pp.  mathnet
    2. A. E. Bondarev, V. A. Galaktionov, “Analiz razvitiya kontseptsii i metodov vizualnogo predstavleniya dannykh v zadachakh vychislitelnoi fiziki”, Preprinty IPM im. M. V. Keldysha, 2009, 053, 28 pp.  mathnet
    3. A. L. Afendikov, A. E. Lutskii, A. V. Plenkin, “Lokalizovannye struktury v idealnoi i vyazkoi modelyakh. Veivletnyi analiz”, Preprinty IPM im. M. V. Keldysha, 2009, 078, 10 pp.  mathnet
    4. A. L. Afendikov, A. E. Lutsky, A. V. Plenkin, “Wavelet study of localised structures in the ideal and viscous models”, Math. Models Comput. Simul., 3:4 (2011), 439–445  mathnet  crossref  mathscinet
    5. A. E. Bondarev, V. A. Galaktionov, V. M. Chechëtkin, “Analysis of the development concepts and methods of visual data representation in computational physics”, Comput. Math. Math. Phys., 51:4 (2011), 624–636  mathnet  crossref  mathscinet  isi
    6. Plenkin A.V., “Kratno-masshtabnyi analiz gazodinamicheskikh polei”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2011, no. 2, 56–59  zmath  elib
    7. A. L. Afendikov, A. E. Lutsky, A. V. Plenkin, “Localization of gas-dynamic fields singularities and adaptation of grid to the singularities position”, Math. Models Comput. Simul., 5:4 (2013), 341–345  mathnet  crossref
    8. A. L. Afendikov, A. E. Lutskii, A. V. Plenkin, “Primenenie veivlet analiza dlya lokalizatsii struktur v raschetakh po idealnoi i vyazkoi modelyam i dlya adaptatsii setok”, Preprinty IPM im. M. V. Keldysha, 2012, 045, 24 pp.  mathnet
    9. A. L. Afendikov, A. E. Lutskii, A. V. Plenkin, “Tekhnologiya adaptivnykh raschetov gazodinamicheskikh techenii na osnove veivlet-analiza”, Preprinty IPM im. M. V. Keldysha, 2014, 110, 30 pp.  mathnet
    10. A. L. Afendikov, K. D. Merkulov, A. V. Plenkin, “Sravnitelnyi analiz podkhodov k chislennomu modelirovaniyu gazodinamicheskikh techenii na dvukhurovnevykh adaptivnykh raschetnykh setkakh”, Preprinty IPM im. M. V. Keldysha, 2015, 095, 24 pp.  mathnet
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