High-order implicit Runge-Kutta time integrators for component-based model reduction of FSI problems

TL;DR

This paper introduces a high-order implicit Runge-Kutta-based model reduction framework for fluid-structure interaction problems, ensuring stability and accuracy for long-term simulations.

Contribution

It develops a novel reduced-order modeling approach combining high-order IRK methods with bubble-port decomposition for FSI problems, maintaining energy balance and stability.

Findings

Stable and accurate reduced models for long-time FSI simulations.

Effective decoupling of interface degrees of freedom.

Preservation of energy balance in reduced models.

Abstract

We propose a model order reduction framework for incompressible fluid-structure interaction (FSI) problems based on high-order implicit Runge-Kutta (IRK) methods. We consider separate reduced spaces for fluid velocity, fluid pressure and solid displacement; we enrich the velocity space with supremizer modes to ensure the inf-sup stability of the fluid subproblem; we consider bubble-port decomposition of fluid velocity and solid displacement to satisfy the kinematic conditions at the fluid structure interface. We resort to Galerkin projection to define the semi-discrete reduced-order model and we consider a Radau-IIA IRK method for time integration: the resulting algebraic system is solved using static condensation of the interface degrees of freedom. The reduced-order model preserves a semi-discrete energy balance inherited from the full-order model, and avoids the need for additional interface enrichment. Numerical experiments demonstrate that the proposed combination of high-order IRK schemes with bubble-port decoupling of velocity and displacement degrees of freedom yields stable and accurate reduced-order model for long-time integration of strongly-coupled parametric FSI problems.