A monolithic one-velocity-field optimal control formulation for fluid-structure interaction problems with large solid deformation

TL;DR

This paper develops a monolithic optimal control approach for fluid-structure interaction systems with large solid deformations, using a one-velocity fictitious domain method and time-dependent control, implemented in FreeFEM++.

Contribution

It introduces a novel monolithic formulation for FSI optimal control with large deformations, combining a one-velocity fictitious domain method and piecewise-in-time control.

Findings

The method is stable across various regularisation parameters.

It effectively reduces the objective function through control of solid velocity.

Numerical experiments demonstrate the approach's efficiency and stability.

Abstract

In this article, we formulate a monolithic optimal control method for general time-dependent Fluid-Structure Interaction (FSI) systems with large solid deformation. We consider a displacement-tracking type of objective with a constraint of the solid velocity, tackle the time-dependent control problems by a piecewise-in-time control, cope with large solid displacement using a one-velocity fictitious domain method, and solve the fully-coupled FSI and the corresponding adjoint equations in a monolithic manner. We implement the proposed method in the open-source software package FreeFEM++ and assess it by three numerical experiments, in the aspects of stability of the numerical scheme for different regularisation parameters, and efficiency of reducing the objective function with control of the solid velocity.