Optimization of Robin-Robin partitioned procedures in Fluid-Structure Interaction Problems

The solution of the Fluid-Structure Interation (FSI) problem, which describes any physical phenomenon where a fluid and a structure interact by exchanging normal stresses through an interface, is problematic, since the fluid and the structure subproblems are coupled through a geometry problem (the unknown interface position) and through the interface continuity of the velocity and of the normal stresses. In many applications featuring a large added mass effect of the fluid on the structure implicit coupling is required to achieve perfect energy balance between fluid and structure at the numerical level. One possible strategy for the solution of such problems is to consider partitioned procedures, that involve separate fluid and structure solvers in an iterative framework. In particular, they interact through the exchange of suitable transmission conditions at the FS interface, and guarantee, at convergence, the satisfaction of the continuity conditions. The introduction of Robin-Robin (RR) partitioned procedures in the framework of FSI problems, as a generalization of the classic Dirichlet-Neumann (DN) scheme, has been motivated to overcome the limitations of the latter algorithm, particularly evident in the presence of large added mass effect, occurring when the fluid and structure densities are similar. We analyze the convergence of partitioned algorithms based on Robin transmission conditions for the solution of linear fluid-structure interaction problems. The convergence analysis allows us to derive a frequency dependent reduction factor at each iteration of the partitioned algorithm, which can be minimized by choosing optimal values of the coefficients in the Robin transmission conditions. Numerical results will be provided, to illustrate the effectiveness of the optimization procedure