Shape optimization of viscous flow field considering fluid-structure-interactive

Abstract

This paper presents numerical solution to a shape optimization of viscous flow field for stationary fluid-structure-interactive (FSI) fields. In the FSI analysis, a weak coupled analysis is used to alternately analyze the governing equations of the flow field domain and the structural field considering geometrically nonlinear. A minimization problem for total dissipation energy is formulated for the shape optimization of viscous flow field in the FSI fields. Shape gradient of the shape optimization problem is derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Reshaping is carried out by the H¹ gradient method proposed as an approach to solving shape optimization problems. For shape optimization of the viscous flow field in the FSI fields, a new shape update method is proposed to overcome separation and interference of the finite element meshes on the common boundary between the flow field and the structural field. Numerical analysis program for the shape optimization problem is developed by using FreeFEM, and the validity of proposed method is confirmed by results of 2D numerical analyses.