Partitioned solution of the unsteady adjoint equations for a strongly coupled fluid-structure interaction problem

Unsteady fluid-structure interaction (FSI) simulations are often time-consuming. As a result, the number of simulations has to be limited in optimisation studies and therefore gradient-based optimisation methods are generally preferred. When the number of optimisation parameters is high, the adjoint equations of the unsteady FSI problem need to be solved to obtain the required gradient at a cost (almost) independent of the number of parameters. In this work, a framework is presented to solve both the forward and the adjoint problem in a partitioned way, which means that the flow equations and the structural equations are solved separately. As an illustration, a one-dimensional example is solved, namely the flow of an incompressible fluid in a straight elastic tube. Due to the strong interaction between the fluid and the structure, quasi-Newton coupling iterations are applied to stabilise the partitioned solution of both the forward and the adjoint problem.