## Modelling of fluid-structure interactions with the space-time finite elements: Solution techniques.(English)Zbl 1144.74044

Summary: The space-time fluid-structure interaction (FSI) techniques developed by the Team for Advanced Flow Simulation and Modeling (T$$_\star$$AFSM) have been applied to a wide range of 3D computation of FSI problems, some as early as in 1994 and many with challenging complexities. In this paper, we review these space-time FSI techniques and describe the enhancements introduced recently by the T$$_\star$$AFSM to increase the scope, accuracy, robustness and efficiency of these techniques. The aspects of the FSI solution process enhanced include the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation, the fluid-structure interface conditions, the preconditioning techniques used in iterative solution of the linear equation systems, and a contact algorithm protecting the quality of the fluid mechanics mesh between the structural surfaces coming into contact. We present a number of 3D numerical examples computed with these new stabilized space-time FSI (SSTFSI) techniques.

### MSC:

 74S05 Finite element methods applied to problems in solid mechanics 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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