A non-overlapping optimization-based domain decomposition approach to component-based model reduction of incompressible flows

TL;DR

This paper introduces a novel domain decomposition and optimization-based model reduction method for efficiently solving parameterized incompressible Navier-Stokes flows, combining interface jump minimization with localized reduced-order models.

Contribution

It develops a non-overlapping optimization-based domain decomposition approach integrated with localized model reduction techniques for improved efficiency in flow simulations.

Findings

Effective interface jump minimization across sub-domains.

Significant computational speed-up with localized training.

Validated accuracy and efficiency through numerical experiments.

Abstract

We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain decomposition technique to determine the control variable that minimizes jumps across the interfaces between sub-domains. To solve the resulting constrained optimization problem, we propose both Gauss-Newton and sequential quadratic programming methods, which effectively transform the constrained problem into an unconstrained formulation. Furthermore, we integrate model order reduction techniques into the optimization framework, to speed up computations. In particular, we incorporate localized training and adaptive enrichment to reduce the burden associated with the training of the local reduced-order models. Numerical results are presented to demonstrate the validity and effectiveness of the overall methodology.