A few techniques to improve data-driven reduced-order simulations for unsteady flows

Abstract

A key step to improve data-driven reduced-order simulations is to compute a transfer function that predicts the time evolution of the reduced-order modes accurately. We demonstrate a couple of useful techniques to achieve this objective: One is to pre-process time-series of reduced-order modes with a low-pass filter, e.g. a polynomial filter and B-spline, and the other is to compute a data-driven transfer function from multiple past time-steps, corresponding to a high-order temporal scheme. These techniques are exercised with POD modes generated from time-resolved planar PIV data. A fully separated flow past the NACA0012 airfoil at the angle of attack of 30∘ and Re=1000 is measured in a water tunnel, and non-periodic unsteady flow is analyzed in two dimensions. From the first 1000 frames, transfer functions are calculated based on minimization of different cost functions, which define least-squares errors in the predicted POD modes at the next time step; subsequently, their prediction capabilities are evaluated during the following 1000 frames based on the accuracy of the predicted POD modes at the next time steps. The multistep schemes can reduce the root-mean-square errors of the predicted mode coefficients by up to 10% without a low-pass filter. Combining a low-pass filter with the second-order temporal scheme can further reduce the errors by 7%, and introduction of an L1-norm constraint for the mode coefficients decreases it by extra 2%. In contrast, nonlinear transfer functions with more degrees of freedom deteriorate the prediction during time duration outside of the sampling period even relative to the linear prediction.