Shape optimization of body located in incompressible viscous flow

Abstract

This paper presents a numerical determination of the optimal shape of body located in the incompressible viscous flow. The optimal shape is defined by the shape which has the minimum fluid force acting on the body. The shape optimization problem is based on an optimal control theory and can be formulated to find out geometrical coordinates of the body to minimize the performance function defined by the force subjected to the body. The performance function should be minimized satisfying the state equation. This problem can be transformed into the minimization problem without constraint condition by the Lagrange multiplier method. As a minimization technique, the gradient-based method is applied. The approximate solution to the flow problem is obtained by the finite element method based on the mixed interpolation with bubble function. In this research, the determination of the minimum fluid force shape in the incompressible Navier–Stokes flow is carried out.

Keywords:

• shape optimization
• finite-element method
• Lagrange multiplier method
• gradient-based method
• fluid force

2000 AMS Subject Classification :

• 49M25
• 49N45
• 68U07
• 76D55
• 58E12