动力学模态分解及其在流体力学中的应用

With the development of computational fluid dynamics, the revelation for the flow structure in unsteady flows becomes much increasingly delicate. This brings a mass of flow information and catalyzes the study of mode extraction to analyze complex dynamic behaviors. This review discusses a representative approach for flow mode extraction, called dynamic mode decomposition (DMD). DMD is a novel technique for modeling flow dynamics from both spatial and temporal data, which becomes popular recently. As a data-driven algorithm, DMD is capable of capturing the frequency and growth rate of flow modes, helping to construct efficient reduced-order models for flow analysis and control. The availability of DMD has been shown in many complex flow phenomena, like turbulence and transition. To improve its robustness, different methodologies have been introduced, including sparsity-promoting, compressive sensing, time-delayed embedding, etc. Moreover, DMD shows a close relationship with Koopman theory (describing the dynamics of a nonlinear system by an infinite-dimensional linear operator) and proper orthogonal decomposition (a well-known technique for analyzing fluid data). In the present paper, the efficacy of DMD has been shown by two test cases: 1) identification of a low-dimensional system, 2) analysis of transonic buffet phenomenon.