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Topological asymptotic formula for the 3D non-stationary Stokes problem and application

Abstract : This paper is concerned with a topological asymptotic expansion for a parabolic operator. We consider the three dimensional non-stationary Stokes system as a model problem and we derive a sensitivity analysis with respect to the creation of a small Dirich-let geometric perturbation. The established asymptotic expansion valid for a large class of shape functions. The proposed analysis is based on a preliminary estimate describing the velocity field perturbation caused by the presence of a small obstacle in the fluid flow domain. The obtained theoretical results are used to built a fast and accurate detection algorithm. Some numerical examples issued from a lake oxygenation problem show the efficiency of the proposed approach.
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https://hal.archives-ouvertes.fr/hal-01851477
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Submitted on : Tuesday, September 22, 2020 - 9:39:53 PM
Last modification on : Wednesday, August 31, 2022 - 12:14:23 PM

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Maatoug Hassine, Rakia Malek. Topological asymptotic formula for the 3D non-stationary Stokes problem and application. Revue Africaine de Recherche en Informatique et Mathématiques Appliquées, 2020, Volume 32 - 2019 - 2021, ⟨10.46298/arima.4760⟩. ⟨hal-01851477v2⟩

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