Speaker
Description
This talk focuses on the numerical analysis of regularized projection-based reduced-order models (ROMs) for turbulent fluid flows. Direct numerical simulations are well known to be computationally infeasible for routine simulations in computational fluid dynamics, particularly at high Reynolds numbers. Reduced-order models offer an efficient low-dimensional framework capable of producing fast and reasonably accurate approximations of the full-order dynamics.
For under-resolved flows, which are typical in high-Reynolds-number regimes, standard POD-ROMs often suffer from loss of accuracy and numerical instability. Regularization techniques based on spatial filtering have been shown to improve both stability and accuracy with negligible additional computational cost. However, depending on the choice of filter and regularization strategy, these methods may introduce excessive numerical diffusion, leading to over-smoothing of the resolved dynamics.
To address this issue, we propose an approximate deconvolution approach designed to recover attenuated flow features and mitigate the over-smoothing effects induced by spatial filtering. The resulting framework enhances ROM accuracy while retaining the stabilizing benefits of regularization. Analytical properties and numerical results are presented to demonstrate the effectiveness of the proposed method for turbulent flow simulations.