Analysis of a time-dependent fluid-structure interaction problem in an optimal control framework over a single time-step

Fluid-structure interaction simulation presents many computational difficulties, particularly when the densities of the fluid and structure are close. A previous report [20] has suggested that recasting the FSI problem in the context of optimal control may significantly reduce computation time. This report introduces a Neumann type control along with detailed analysis for the stability and existence of an optimal solution for a given time-step. The existence of Lagrangian multipliers is proved, and an optimality system is derived. A gradient based optimization algorithm is then presented with numerical results confirming its effectiveness in computing an accurate solution.