Shape Sensitivity Analysis of a 2D Fluid-Structure Interaction Problem

We study the shape differentiability of a general functional depending on the solution of a bidimensional stationary Stokes-elasticity system with small loads, with respect to the reference domain of the elastic structure immersed in a viscous fluid. The differentiability with respect to reference elastic domain variations is considered under shape perturbations with diffeomorphisms. The shape derivative is then calculated with the use of the velocity method. This derivative involves the material derivatives of the solution of this fluid-structure interaction problem. The adjoint method is then used to obtain a simplified expression for the shape derivative.

Automated summary

In this study, we investigate the shape differentiability of a general functional that depends on the solution of a stationary Stokes-elasticity system in two dimensions with small loads. We consider the differentiability with respect to variations in the reference elastic domain using shape perturbations with diffeomorphisms. The shape derivative is calculated using the velocity method, involving the material derivatives of the solution of the fluid-structure interaction problem. The adjoint method is then applied to obtain a simplified expression for the shape derivative.