On free surface PDE constrained shape optimization problems

Shape optimization problems in fluid dynamics governed by the free surface flows are considered. Such problems are inspired by the process of continuous casting of steel where optimization of large vortex structures in different metallurgical reactors is of paramount importance to ensure good quality output. The pseudo-transient approach is used as solution strategy for solving the free surface problem. Design sensitivities involving different cost functionals are derived using a formal Lagrangian framework. Numerical results are presented which indicate the success of the proposed algorithm for solving this free surface shape optimization problem.