Shape reconstruction of the object immersed in the incompressible fluid flow

In this paper, we present a formulation and numerical results of the shape reconstruction of the object immersed in the incompressible fluid flow. The cost functional should be minimized satisfying the Naiver-Stokes equations. The Shape sensitivity analysis of the cost functional was derived based on the adjoint method. The level set method is successfully utilized as the minimization algorithm, which is implemented in an Eulerian framework, therefore the computational cost is moderate. For the numerical study, the optimal shape of the body which has a rectangle shape as an initial state can be finally obtained as the circular target shape.