报告题目 (Title)：High-order implicit Runge-Kutta time integrators for component-based model reduction of FSI problems
（面向流固耦合问题组件式模型降阶的高阶隐式龙格-库塔时间积分方法）
报告人 (Speaker)：张磊 助理教授（同济大学）
报告时间 (Time)：2026年4月25日（周六）14:00-14:30
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：纪丽洁
主办部门：理学院数学系
摘要：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.
