Multiphysics mode synthesis of fluid–structure interaction with free surface

A new component mode synthesis (CMS) is introduced for reduced-order modeling of fluid–structure interaction (FSI) with a free surface. The components imply parts of structures in the CMS method of conventional structural vibration, but they are mono-physics domains in multiphysics problems. Therefore, unlike the original CMS, the interface constraint modes for multiphysics need to be newly defined to reflect the interaction between different physics, which is realized by a sequential model reduction scheme, which is known as multiphysics mode synthesis (MMS). This study addresses a widely used asymmetric (u, p) formulation that comprises structural displacement (u) and fluid pressure (p) including free surface and interior fluid. In carrying out the proposed sequential MMS, the structural part is first reduced, and then, a newly refined coupling matrix including structural modal effects is added to the fluid matrices. The fluid part is then reduced with the updated matrices. Consequently, accuracy improvement of the reduced matrices is achieved while preserving the strongly coupled effect in the proposed MMS, and the numerical instabilities in the model reduction process are alleviated. Better computational efficiency of the reduction process is also achieved by ignoring the higher order coupling terms that have numerically less effect. The performance of the proposed MMS is illustrated through numerical examples.