Two-stage Self-Updating Unsteady POD-ROM Based on Least Squares Residual Minimization

Nowadays, reduced-order model techniques are widely adopted in the aerospace field to reduce computational cost of unsteady fluid-dynamics simulations without causing a perceivable degradation in prediction accuracy. Indeed, aerodynamic analyses involving non-linear phenomena usually require complex numerical solvers, thereby resulting in simulation turnaroundtimes that are often too long for preliminary design process applications or to directly interact with other disciplines. Among all the proposed reduced-order model techniques, the ones based on proper orthogonal decomposition of high-fidelity data and least-square minimization of full-order model unsteady residuals have been found to accurately and efficiently predict unsteady flowfields around airfoils and aircraft. However, the training process of such techniques is affected by two main problems: the burden of defining a-priori the set of high-fidelity simulations that have to be run to create the training dataset, and the redundant amount of information contained in it due to the small time-step size required to ensure stability and convergence of the unsteady simulations. This paper tries to mitigate these two downsides by proposing a self-updating unsteady framework for reduced-order models based on proper orthogonal decomposition. The framework takes advantage of the full-order model unsteady residual resulting from the least-square minimization to determine when the predicted solution does not meet the accuracy requirements defined by the user. In this case, the computational fluid dynamics (CFD) solver is run to improve the predicted solution, and the final CFD result is used to update the underlying reduced solution space of the reduced-order model. The goal is to create a reduced-order model self-updating framework able to maintain the effectiveness of algorithms based on proper orthogonal decomposition, but also to reduce the overall training time and enhance the model flexibility in simulating new phenomena. The proposed technique is tested for the prediction of flowfields around a pitching airfoil with a linear chirp and harmonic oscillator signals at transonic conditions