The role of a structural mode shape based interaction law to suppress added mass instabilities in partitioned strongly coupled elastic structure-fluid systems

The physical level of interaction between fluid and structure can be either one-way or two-way depending on the direction of information exchange at the interface of fluid and solid. The former can be solved by a partitioned approach and weak coupling. In problems involving two-way fluid-structure interaction, using a partitioned approach and strong coupling, sometimes stability restriction is encountered. This is an artificial added mass effect, which is independent of the numerical time step. Unfortunately an accurate and efficient method to deal with all the different levels of interaction is scarce. Conventionally, relaxation is applied to remedy this problem. The computational cost is directly related to number of sub-iterations between fluid and structural solver at each time step. In this study, the source of this instability is investigated. A discrete representation of a basic added mass operator is given and instability conditions are assessed. A new method is proposed to relax this restriction, the idea essentially is to remove the instability source from the structure and move it to the fluid and solve it monolithically with the fluid. We call this an interaction law. An estimate of the structural response is derived from structural mode shapes. As a test case, a 2D dam break problem interacting with an elastic vertical flexible beam is selected. The interaction of fluid with the beam undergoes several stages. The breaking waves on the beam can increase the added mass drastically, therefore the added mass ratio increases as well. In such a cases, the asset of interaction law is better elaborated, while the stability condition requires very high relaxation without interaction law, but the relaxation can be lowered by only using first five beam mode shapes. As a consequence, the number of sub-iterations reduces by one order. The numerical observations confirm the reduction in computational time due to utilization of the interaction law.