Adjoint-based methods for optimization and goal-oriented error control applied to fluid-structure interaction: implementation of a partition-of-unity dual-weighted residual estimator for stationary forward FSI problems in deal.II

TL;DR

This paper develops and implements an adjoint-based goal-oriented error estimator for stationary fluid-structure interaction problems, enabling efficient mesh adaptivity and accurate computation of quantities like displacements, drag, and lift.

Contribution

It introduces a partition-of-unity dual-weighted residual estimator for FSI problems within a variational-monolithic framework, with open-source implementation in deal.II.

Findings

Effective error control for FSI quantities of interest

Open-source implementation available on GitHub

Enhanced mesh adaptivity improves solution accuracy

Abstract

In this work, we implement goal-oriented error control and spatial mesh adaptivity for stationary fluid-structure interaction. The a posteriori error estimator is realized using the dual-weighted residual method in which the adjoint equation arises. The fluid-structure interaction problem is formulated within a variational-monolithic framework using arbitrary Lagrangian-Eulerian coordinates. The overall problem is nonlinear and solved with Newton's method. We specifically consider the FSI-1 benchmark problem in which quantities of interest include the elastic beam displacements, drag, and lift. The implementation is provided open-source published on github https://github.com/tommeswick/goal-oriented-fsi. Possible extensions are discussed in the source code and in the conclusions of this paper.