An optimal control method for time-dependent fluid-structure interaction problems

In this article, we derive an adjoint Fluid-Structure Interaction (FSI)system in an Arbitrary Lagrangian-Eulerian (ALE) framework, based upon a one-field finite element method. A key feature of this approach is that the interfacecondition is automatically satisfied and the problem size is reduced since we onlysolve for one-velocity field for both the primary and adjoint system. A velocity(and/or displacement)-matching optimisation problem is considered by controllinga distributed force. The optimisation problem is solved using a gradient descentmethod, and a stabilised Barzilai-Borwein method is adopted to accelerate theconvergence, which does not need additional evaluations of the objective func-tional. The proposed control method is validated and assessed against a series ofstatic and dynamic benchmark FSI problems, before being applied successfully tosolve a highly challenging FSI control problem.