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arXiv · 2412.18916

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

Tommaso Taddei·Xuejun Xu·Lei Zhang
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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.

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Tommaso Taddei, Xuejun Xu, Lei Zhang. 2024-12-25. Optimization-based model order reduction of fluid-structure interaction problems. https://arxiv.org/abs/2412.18916

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