Analysis of Pulsating Gas-Dynamic Flows Using Proper Orthogonal Decomposition

This work is devoted to the development of algorithmic tools for extracting stable structures (modes, coherent structures) associated with oscillations in unsteady gas-dynamic fields. The research area related to modal decomposition is actively developing, since it has a number of advantages over traditional methods for processing data obtained from numerical or physical experiments. This work uses one of the well-established methods of modal analysis, namely Proper Orthogonal Decomposition (POD). The method consists in representing the pulsating part of a field as a sum of products of temporal and spatial modes (basis functions), each of which approximates the field in the sense of the best quadratic approximation; this makes it possible to interpret such modes as the most significant flow structures within the chosen measure. Finding the basis functions on a grid is based on methods of linear algebra and is reduced to finding the right and left singular vectors of the singular value decomposition (SVD) of a matrix containing field distributions at fixed time instants. The algorithm was tested on a model problem. Numerical studies were then carried out for two-dimensional flows arising when a gas medium flows around bodies of different shapes (a square cylinder and a NACA 0012 airfoil), in regimes where a von Karman vortex street is formed.