Optimization-based model order reduction of fluid-structure interaction problems

TL;DR

This paper presents an optimization-based approach for full-order and reduced-order modeling of fluid-structure interaction problems, utilizing implicit coupling and projection-based model reduction techniques.

Contribution

It introduces a novel optimization-based coupled formulation for fluid-structure interaction and applies projection-based model reduction to both fluid and solid subproblems.

Findings

Effective coupling of fluid and solid models demonstrated

Projection-based reduction reduces computational cost

Numerical results validate the approach

Abstract

We introduce optimization-based full-order and reduced-order formulations of fluid structure interaction problems. We study the flow of an incompressible Newtonian fluid which interacts with an elastic body: we consider an arbitrary Lagrangian Eulerian formulation of the fluid problem and a fully Lagrangian formulation of the solid problem; we rely on a finite element discretization of both fluid and solid equations. The distinctive feature of our approach is an implicit coupling of fluid and structural problems that relies on the solution to a constrained optimization problem with equality constraints. We discuss the application of projection-based model reduction to both fluid and solid subproblems: we rely on Galerkin projection for the solid equations and on least-square Petrov-Galerkin projection for the fluid equations. Numerical results for three model problems illustrate the many features of the formulation.