On the topological gradient method for a nonlinear problem

The aeration process via diffuser is used to combat the lack of oxygen in water reservoirs due to the eutrophication problem. The optimization of the diffuser location allowing better flow dynamic permit to remedy this phenomenon and improve the water quality. We propose to adapt the topological gradient method to this problem. The idea consists of studying the topological sensitivity analysis of the considered model based on the time dependent Navier-Stokes equation with respect to the insertion of a diffuser in the flow domain. Various numerical tests are presented to validate the used approach.