Optimization with nonstationary, nonlinear monolithic fluid-structure interaction

TL;DR

This paper develops a gradient-based optimization framework for nonlinear, nonstationary fluid-structure interaction problems using a monolithic approach and adjoint methods, demonstrated through numerical benchmarks.

Contribution

It introduces a monolithic optimization approach for nonlinear, nonstationary FSI problems with adjoint-based gradients and demonstrates its effectiveness on benchmark tests.

Findings

Successful application to fluid-structure benchmarks

Effective gradient computation via adjoint methods

Robust Newton-based solution for nonlinear subproblems

Abstract

Within this work, we consider optimization settings for nonlinear, nonstationary fluid-structure interaction. The problem is formulated in a monolithic fashion using the arbitrary Lagrangian-Eulerian framework to set-up the fluid-structure forward problem. In the optimization approach, either optimal control or parameter estimation problems are treated. In the latter, the stiffness of the solid is estimated from given reference values. In the numerical solution, the optimization problem is solved with a gradient-based solution algorithm. The nonlinear subproblems of the FSI forward problem are solved with a Newton method including line search. Specifically, we will formally provide the backward-in-time running adjoint state used for gradient computations. Our algorithmic developments are demonstrated with some numerical examples as for instance extensions of the well-known fluid-structure benchmark settings and a flapping membrane test in a channel flow with elastic walls.