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 improve 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.

Publication: 

JOURNAL OF COMPUTATIONAL PHYSICS

http://dx.doi.org/10.1016/j.jcp.2026.115326

Author:

Tommaso Taddei

Dipartimento di Matematica, Sapienza University of Rome, 00185, Rome, Italy

Email addresses: tommaso.taddei@uniroma1.it

Xuejun Xu

School of Mathematical Sciences, Key Laboratory of Intelligent Computing and Applications (Ministry of Education), Tongji University, Shanghai, 200092, China

Institute of Computational Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100190, China

Email addresses: xxj@lsec.cc.ac.cn

Lei Zhang

School of Mathematical Sciences, Key Laboratory of Intelligent Computing and Applications (Ministry of Education), Tongji University, Shanghai, 200092, China

Corresponding author

Email addresses:22210@tongji.edu.cn