Shape optimization of viscous flow field considering Fluid-Structure-Interactive(FSI) problem

Abstract

This paper presents numerical solution to shape optimization for fluid structure interactive fields. A minimization problem for total dissipation energy in viscous flow field is formulated for the shape optimization. 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 traction method proposed as an approach to solving shape optimization problems. Numerical analysis program for the shape optimization problem is developed based on FreeFem++, and the validity of proposed method is confirmed by results of 2D numerical analyses.