Partitioned simulation strategies for fluid–structure–control interaction problems by Gauss–Seidel formulations

In this contribution the multi-physics problem of fluid–structure–control interaction (FSCI) is solved by an iterative, partitioned approach utilizing Gauss–Seidel formulations. The aim is to conduct a fully coupled co-simulation of the FSCI problem, where the controller actively influences the dynamics of the structure. The purpose of this manuscript is twofold: In the first part, in order to get a profound idea of the behavior and parametric sensitivity of such systems involving multiple couplings, the simplified model problem introduced for fluid–structure interaction (FSI) by Joosten, Dettmer and Perić is extended by a generic control unit. Since a monolithic solution for this simplified model problem can be found, it is used for first investigations concerning solvability and stability. On this basis, three different variants for coupling the subsystems fluid, structure and controller by a Gauss–Seidel scheme, are derived and systematically investigated. More precisely the FSCI problem is solved without nesting of the subsystems in the first variant and with nesting of two of the respective subsystems in the second and third variant. In the second part, the resulting algorithms are applied to a complex, non-linear, multi-degree of freedom problem, which is a well-known benchmark problem in the FSI community and is therefore extended to FSCI. Applying those algorithms to the multi-degree of freedom problem shows good results and substantiates the applicability to such problems. It follows, actively influencing the dynamics of the structure in the FSCI problem by a controller reduces the structural vibrations induced by the fluid flow significantly.