  In this paper, a type of novel projection-based, time-segmented reduced order
model (ROM) is proposed for dynamic fluid-structure interaction (FSI) problems
based upon the arbitrary Lagrangian--Eulerian (ALE)-finite element method (FEM)
in a monolithic frame, where spatially, each variable is separated from others
in terms of their attribution (fluid/structure), category (velocity/pressure)
and component (horizontal/vertical) while temporally, the proper orthogonal
decomposition (POD) bases are constructed in some deliberately partitioned time
segments tailored through extensive numerical trials. By the combination of
spatial and temporal decompositions, the developed ROM approach enables
prolonged simulations under prescribed accuracy thresholds. Numerical
experiments are carried out to compare numerical performances of the proposed
ROM with corresponding full-order model (FOM) by solving a two-dimensional FSI
benchmark problem that involves a vibrating elastic beam in the fluid, where
the performance of offline ROM on perturbed physical parameters in the online
phase is investigated as well. Extensive numerical results demonstrate that the
proposed ROM has a comparable accuracy to while much higher efficiency than the
FOM. The developed ROM approach is dimension-independent and can be seamlessly
extended to solve high dimensional FSI problems.
