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Paper details
Number 1 - March 2025
Volume 35 - 2025
On robustness to a topological perturbation in fluid mechanics
Merwan Abdelbari, Khadra Nachi, Jan Sokołowski, Antonio Andre Novotny
Abstract
The robustness to topological perturbations in geometrical domains filled by a fluid flowing in Stokes–Darcy regime is
considered. The cost functional is given by the energy dissipation in the fluid. The topological perturbation is carried out by
the nucleation of an infinitesimal circular obstacle, which can be considered as a small measurement device. Our approach
is based on the topological derivative method, which has been previously employed in the shape and topology optimization
problems. The topological derivative (TD) measures the sensitivity of a given shape functional with respect to topological
domain perturbations. The TD is used to determine the location of the small device placement, through a distributed control
problem. By taking into account the effect of the disturbance term or uncertain input data in the TD expression, the problem
of robustness to topological perturbation for the energy functional can be formulated as a minimax optimization problem
with a pointwise observation. Numerical examples illustrate the efficiency of the proposed topological derivative method.
Keywords
topological derivative, shape optimization, optimal control, robust control