Shape sensitivity of a 2D Fluid-Structure Interaction problem between a viscous incompressible fluid and an incompressible elastic structure

2022/10/12 by Valentin Calisti, Calisti, V., I Lucardesi +3
Chemical Engineering · Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #FOS: Mathematics #Optimization and Control (math.OC) #Rheology and Fluid Dynamics Studies

paper · pdf · doi:10.48550/arxiv.2210.05850

openalex publication_date 2022/10/12 · openalex created_date 2022/10/14 · openalex updated_date 2026/07/28

Abstract

We study the shape differentiability of a general functional depending on the solution of a bidimensional stationary Stokes-Elasticity system, with respect to the reference domain of the elastic structure immersed in a viscous fluid. The differentiability with respect to reference elastic domain variations are 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 used to obtain a simplified expression for the shape derivative.

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