A dynamic closure modeling framework for model order reduction of geophysical flows

Abstract: In this paper, a dynamic closure modeling approach has been derived to stabilize the projection-based reduced order models in the long-term evolution of forced-dissipative dynamical systems. To simplify our derivation without losing generalizability, the proposed reduced order modeling (ROM) framework is first constructed by Galerkin projection of the single-layer quasi-geostrophic equation, a standard prototype of large-scale general circulation models, onto a set of dominant proper orthogonal decomposition (POD) modes. We then propose an eddy viscosity closure approach to stabilize the resulting surrogate model considering the analogy between large eddy simulation (LES) and truncated modal projection. Our efforts, in particular, include the translation of the dynamic subgrid-scale model into our ROM setting by defining a test truncation similar to the test filtering in LES. The a posteriori analysis shows that our approach is remarkably accurate, allowing us to integrate simulations over long time intervals at a nominally small computational overhead.