Abstract

In this work, we propose a novel resid-ual based data driven closure strategy for reduced-order models (ROMs) of under-resolved, convection-dominated flows. The proposed closure model is developed within a variational multiscale (VMS) framework, leveraging available full order model (FOM) data and an ansatz that explicitly depends on the ROM residual. We emphasize that this approach is fundamentally different from existing data driven ROM closure models, which typically rely on the ROM coefficients as inputs. In contrast, the proposed residual based method utilizes the ROM residual to account for the effects of unresolved scales. We assess the performance of the proposed residual-based data-driven VMS-ROM in the numerical simulation of two-dimensional flow past a cylinder at Reynolds number Re = 1000. The results demonstrate that the proposed method yields significantly improved accuracy compared to standard coefficient based data driven VMS-ROM approaches.