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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.

Source : oai:HAL:hal-01851477v2

Volume: Volume 32 - 2019 - 2021

Published on: October 22, 2020

Accepted on: September 28, 2018

Submitted on: August 17, 2018

Keywords: Topological asymptotic expansion,non-stationary Stokes system,calculus of variations,lake oxygenation problem,topology optimization,calcul de variations,système de Stokes,optimisation topologique,Analyse de sensitivité topologique,[MATH]Mathematics [math],[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC],[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]

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