Data-driven reduced order modeling for parametrized time-dependent flow problems

Abstract

This paper proposes a nonintrusive reduced basis (RB) method based on dynamic mode decomposition (DMD) for parameterized time-dependent flows. In the offline stage, the reduced basis functions are extracted by a two-step proper orthogonal decomposition algorithm. Then, a novel hybrid DMD regression model that combines windowed DMD and optimized DMD is introduced for the temporal evolution of the RB coefficients. To improve the stability of this method for complex nonlinear problems, we introduce a threshold value to modify the DMD eigenvalues and eigenvectors. Moreover, the interpolation of the coefficients in parameter space is conducted by a feedforward neural network or random forest algorithm. The prediction of the RB solution at a new time/parameter value can be recovered at a low computational cost in the online stage, which is completely decoupled from the high-fidelity dimension. We demonstrate the performance of the proposed model with two cases: (i) laminar flow past a two-dimensional cylinder and (ii) turbulent flow around a three-dimensional SD7003 airfoil. The results show reasonable efficiency and robustness of this novel reduced-order model.