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 interface condition is automatically satisfied and the problem size is reduced since we only solve for one velocity field for both the primary and adjoint system. A velocity (and/or displacement)-matching optimisation problem is considered by controlling a distributed force. The optimisation problem is solved using a gradient descent method, and a stabilised Barzilai-Borwein method is adopted to accelerate the convergence, which does not need additional evaluations of the objective functional. The proposed control method is validated and assessed against a series of static and dynamic benchmark FSI problems, before being applied successfully to solve a highly challenging FSI control problem.

Automated summary

This article presents an adjoint fluid-structure interaction system in an arbitrary Lagrangian-Eulerian framework, based on a one-field finite element method. The key feature of this approach is automatic satisfaction of interface conditions and reduced problem size due to solving for only one velocity field. A velocity (and/or displacement)-matching optimization problem is considered by controlling a distributed force, solved using a gradient descent method and a stabilised Barzilai-Borwein method for faster convergence without additional evaluations.