Geodesic
Localization of singularities in gas-dynamic fields with the aid of wavelet analyses
Matematičeskoe modelirovanie, Tome 20 (2008) no. 7, pp. 65-84

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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. 
@article{MM_2008_20_7_a6,
     author = {A. L. Afendikov and L. I. Levkovich-Maslyuk and A. E. Lutsky and A. V. Plenkin},
     title = {Localization of singularities in gas-dynamic fields with the aid of wavelet analyses},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {65--84},
     publisher = {mathdoc},
     volume = {20},
     number = {7},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2008_20_7_a6/}
}
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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/