Shape Sensitivity Analysis of a 2D Fluid–Structure Interaction Problem

Valentin Calisti (), Ilaria Lucardesi () and Jean-François Scheid ()
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Valentin Calisti: Institute of Mathematics of the Czech Academy of Sciences
Ilaria Lucardesi: Dipartimento di Matematica e Informatica, Università degli Studi di Firenze
Jean-François Scheid: Université de Lorraine

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 1, No 2, 36-79

Abstract: Abstract We study the shape differentiability of a general functional depending on the solution of a bidimensional stationary Stokes–elasticity system with small loads, with respect to the reference domain of the elastic structure immersed in a viscous fluid. The differentiability with respect to reference elastic domain variations is considered under shape perturbations with diffeomorphisms. The shape derivative is then calculated with the use of the velocity method. This derivative involves the material derivatives of the solution of this fluid–structure interaction problem. The adjoint method is then used to obtain a simplified expression for the shape derivative.

Keywords: Fluid–structure system; Stokes and elasticity equations; Shape optimisation; Shape sensitivity (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02213-4

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