Localization of singularities of gas dynamics fields with the aid of complex and real wavelets
Three methods of construction of the detector are suggested in order to localize singularities in gas dynamics fields. The basic idea is to switch from the initial field to its wavelet-transform and to use various characteristics of the transformed field as indicators of existence of singularities. The first detector is based on the approximation of the Laplacian of the initial field. The second one is the direct generalization of the detector designed in the previous works of the authors - tracking the phase jumps of the complex wavelet-transform - on the case of any pairs of real orthogonal wavelet filters. The third detector carries out the classification of points of the field (distinguishing areas of a regularity, strong and weak shock waves) on the basis of the estimation of a local parameter of the Lipschitz regularities. Orthogonal real and complex Daubechies wavelets were used in calculations. The description of the method and the numerical experiments were given.
Mathematical problems and theory of numerical methods