Partitioned solution of an unsteady adjoint for strongly coupled fluid-structure interactions and application to parameter identification of a one-dimensional problem

Unsteady fluid-structure interaction (FSI) simulations are generally time-consuming. Gradient-based methods are preferred to minimise the computational cost of parameter identification studies (and more in general optimisation) with a high number of parameters. However, calculating the cost function’s gradient using finite differences becomes prohibitively expensive for a high number of parameters. Therefore, the adjoint equations of the unsteady FSI problem are solved to obtain this gradient at a cost almost independent of the number of parameters. Here, both the forward and the adjoint problems are solved in a partitioned way, which means that the flow equations and the structural equations are solved separately. The application of interest is the identification of the arterial wall’s stiffness by comparing the motion of the arterial wall with a reference, possibly obtained from non-invasive imaging. 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.