Multi-fidelity surrogate reduced-order modeling of steady flow estimation

A multi-fidelity reduced-order model (ROM), which incorporates low-fidelity data to improve the prediction of high-fidelity results, is proposed for the reconstruction of steady flow field at different conditions. The spatial basis functions of low-fidelity and high-fidelity data, which are generated for all training sets are extracted separately by proper orthogonal decomposition. Then a surrogate model is used to construct mappings between the mode coefficients obtained from low-fidelity and the high-fidelity data. In the online stage, both the low-fidelity flow at the predicted state and the surrogate model are needed to predict the mode coefficients of the high-fidelity flow, and the high-fidelity flow field is subsequently reconstructed. This method differs from existing surrogate-based reduced-order modeling method because it allows the use of partial physical information for flow estimation, which is coming from the low-fidelity data instead of adopting a black-box mapping between system state and the projection coefficients. Numerical studies are presented for a lid-driven cavity problem and transonic flow past a NACA0012 airfoil. Two low-fidelity models, with either a coarse mesh or a lower numerical order, are considered respectively. Results show that the proposed multi-fidelity ROM predicts the flow field accurately and outperforms the traditional methods in both interpolated and extrapolated conditions.