Localization of Singularities of Gas Dynamics Fields with the Aid of Complex Orthogonal Wavelet Transform.
A new approach to determination of singularity lines and surfaces in gas dynamics fields (density, pressure, velocity) is suggested. The main idea is to look at the complex-valued wavelet transform of the given gas dynamics flow, and use jumps of the phase as indicators of the singularity location. In our experiments we used orthogonal wavelet transform (OWT) with 2 variants of complex-valued wavelets from Daubechies family, DCOLA8 and DCOMS22, defined by filters with 8 and 22 coefficients, respectively. It turned out that lines were the phase of OWT varies rapidly are very close to the physical singularities of the flow, such as shock waves, and contact and weak discontinuities. Standard edge detection techniques applied to the OWT phase fields allowed to obtain the complete map of singularities of the flow. Since OWT is computed by a fast algorithm (linear in input data volume), such a method of singularities localization can be used in real time in parallel with gas dynamics computations. Descriptions of the method and experiments are outlined.
Mathematical problems and theory of numerical methods