Kawahara Lab. Shape Optimization of a Body Located in the Incompressible Naiver-Stokes Flow

The purpose of this study is to obtain an optimal shape of a body located in the incompress-ible viscous flow by the finite element method. As the state equation, the Navier-Stokes equation in the non-dimensional form is applied. The optimal shape is defined so as to minimize a fluid force which is divided into the drag and lift forces acting on the body. The shape optimization based on an optimal control theory is formulated to find out the surface coordinates of the body. This problem can be transformed into the minimization problem without constraint condition by the Lagrange multiplier method. As the minimization technique, the gradient-based method is applied. Based on the triangular structured finite element mesh, the gradient is obtained based on the adjoint equation. The minimum fluid force shape is obtained at Reynolds number 250 flow