Dynamic mode decomposition with exogenous input for data-driven modeling of unsteady flows

This work proposes a data-driven reduced-order modeling algorithm for complex, high-dimensional, and unsteady fluid systems with exogenous input and control. This algorithm is a variant of dynamic mode decomposition (DMD), which is an equation-free method for identifying coherent structures and modeling complex flow dynamics. Compared with existing methods, the proposed method improves the capability of predicting the flow evolution near the unstable equilibrium state. The method is achieved by two steps. First, the system matrix without input is identified by standard DMD to represent the intrinsic flow dynamics. Second, the input term, represented by a state space equation, is identified through existing methods for DMD with control effects. The whole system with input is described by the superposition of both the system matrix and the input term. The proposed method is validated by one simple two-dimensional dynamic system and two test cases of unsteady flow, including flow past a circular cylinder at Reynolds number 45 and flow past a NACA0012 airfoil at an angle of attack 25°. Results indicate that the proposed method gives more accurate description on the flow evolution with or without external forcing.