On the application of the dynamic mode decomposition in problems of computational fluid dynamics

The Dynamic mode decomposition (DMD) method is an algorithm for searching for an evolution operator (inverse operator problem solutions) in a finite-dimensional problem solution space (numerical or experimentally obtained) in a set of solutions (slices, 'snapshots') in some consecutive moments of time. Expansion of the phase space due to the use of a nonlinear basis (relative to the variables of the problem) allows us to construct a global linear operator describing a linear evolution in the extended 'rectifying space' (the Coopman operator) and the Perron–Frobenius operator that is its adjoint one. The DMD method is equivalent to a compressed representation of a linear evolution operator in the form of a product of rectangular matrices, which provides significant savings in the required memory during calculations. The main properties and possibilities of the DMD method are considered. The results of DMD application to nonlinear nonstationary two-dimensional flow of compressible inviscid gas are presented.