Optimisation-Based Coupling of Finite Element Model and Reduced Order Model for Computational Fluid Dynamics

Abstract: Using Domain Decomposition (DD) algorithm on non--overlapping domains, we compare couplings of different discretisation models, such as Finite Element (FEM) and Reduced Order (ROM) models for separate subcomponents. In particular, we consider an optimisation-based DD model where the coupling on the interface is performed using a control variable representing the normal flux. We use iterative gradient-based optimisation algorithms to decouple the subdomain state solutions as well as to locally generate ROMs on each subdomain. Then, we consider FEM or ROM discretisation models for each of the DD problem components, namely, the triplet state1-state2-control. On the backward-facing step Navier-Stokes (NS) problem, we investigate the efficacy of the presented couplings in terms of optimisation iterations, optimal functional values and relative errors.