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Control of a mechanical aeration process via topological sensitivity analysis. (English) Zbl 1162.76019

Summary: The topological sensitivity analysis method gives the variation of a criterion with respect to the creation of a small hole in the domain. In this paper, we use this method to control the mechanical aeration process in eutrophic lakes. A simplified model based on incompressible Navier-Stokes equations is used, only considering the liquid phase, which is the dominant one. The injected air is taken into account through local boundary conditions for the velocity, on the injector holes. A 3D numerical simulation of the aeration effects is proposed using a mixed finite element method. In order to generate the best motion in the fluid for aeration purposes, the optimization of the injector location is considered. The main idea is to carry out topological sensitivity analysis with respect to the insertion of an injector. Finally, a topological optimization algorithm is proposed and some numerical results, showing the efficiency of our approach, are presented.

MSC:

76D55 Flow control and optimization for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
76T10 Liquid-gas two-phase flows, bubbly flows
76M10 Finite element methods applied to problems in fluid mechanics
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