The authors previously developed the algorithm based on wavelet analysis, allowing one to localize singularities in calculations of gas-dynamic flows, which are obtained by using shock-capturing methods. The efficiency of applying the specified algorithm for adapting the grid to the position of the flow singularities is shown. In particular, analogs of shock waves existing when simulating the flow on an ideal model are localized during research on the structure of viscous 3D flow at large Reynolds numbers.

The features identified by the wavelet algorithm based on Euler and Reynolds model calculations with the k-ɛ model of turbulence and the use of methods of through count are analyzed. The studies have shown that in a viscid fluid, the structures corresponding to shock waves in an ideal fluid are clearly manifested, and on them the Hugoniot conditions are fulfilled to a high accuracy. Besides, the additional structures corresponding to vortices, as well as boundary and mixing layers, are localized in the viscid fluid.

On the basis of numerical data processing, it is shown that a joint analysis of singularities detected in an initial gas dynamic field and at the first level of its wavelet decomposition allows one to remove the most part of numerical artifacts caused by numerical errors in computations. The application of asymmetric wavelets for this decomposition leads to a displacement of discontinuities. It is also shown that the values of the field can be identified with the coefficients of its wavelet decomposition.