High-order implicit Runge-Kutta time integrators for component-based model reduction of FSI problems
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| Format: | Preprint |
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2025
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| _version_ | 1866909977650659328 |
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| author | Taddei, Tommaso Xu, Xuejun Zhang, Lei |
| author_facet | Taddei, Tommaso Xu, Xuejun Zhang, Lei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23363 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-order implicit Runge-Kutta time integrators for component-based model reduction of FSI problems Taddei, Tommaso Xu, Xuejun Zhang, Lei Numerical Analysis 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. |
| title | High-order implicit Runge-Kutta time integrators for component-based model reduction of FSI problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2512.23363 |