Shape design for controlling flow velocity distribution of viscous flow field considering fluid–structure interaction

Abstract

This study presents a numerical solution to the shape design problem in a viscous flow field that considers fluid–structure interactions. The square error integrals between the actual flow velocity distributions and the target distributions used to control the flow velocity of the subdomain in the viscous flow field are used as the objective functional. The adjoint variable method is used. A shape derivative is derived for this problem. Furthermore, the H¹ gradient method is used to perform reshaping. A numerical analysis program is developed for the problem using FreeFEM, and its validity is confirmed using the numerical results of 2D problems.