Free surfaces: shape sensitivity analysis and numerical methods

Trial Methods for Nonlinear Bernoulli Problem

In this article we consider a free boundary problem which is related to formation of waves on a fluid surface (for example the ship waves). We study the possibility to construct ‘trial’ methods where one solves a sequence of standard flow problems formulated in different geometries that converge to the final free boundary. Furthermore, we use the shape optimization techniques to analyse the convergence of the fixed point iteration near a fixed point. For stream function case we conclude that the fast convergence can be obtained by using non-standard boundary conditions and we present numerical results to confirm the analysis.