Shape reconstruction of an inverse boundary value problem of two-dimensional Navier-Stokes equations

This paper is concerned with the problem of the shape reconstruction of two-dimensional flows governed by the Navier-Stokes equations. Our objective is to derive a regularized Gauss-Newton method using the corresponding operator equation in which the unknown is the geometric domain. The theoretical foundation for the Gauss-Newton method is given by establishing the differentiability of the initial boundary value problem with respect to the boundary curve in the sense of a domain derivative. The numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible.