A new hybrid reduced order modeling for parametrized Navier–Stokes equations in stream-vorticity formulation

Abstract

In the context of traditional reduced order modeling methods (ROMs), time and parameter extrapolation tasks remain a formidable challenge. To this end, we propose a hybrid projection/data-driven framework that leverages two subspaces to improve the prediction accuracy of traditional ROMs. We first obtain inaccurate mode coefficients from traditional ROMs in the reduced order subspace. Then, in the prior dimensionality reduced subspace, we correct the inaccurate mode coefficients and restore the discarded mode coefficients through neural network. Finally, we approximate the solutions with these mode coefficients in the prior dimensionality reduced subspace. To reduce the computational cost during the offline training stage, we propose a training data sampling strategy based on dynamic mode decomposition (DMD). The effectiveness of the proposed method is investigated with the parameterized Navier–Stokes equations in stream-vorticity formulation. In addition, two additional time extrapolation methods based on DMD are also proposed and compared.