Shape sensitivity analysis of time-dependent flows of incompressible non-Newtonian fluids

TL;DR

This paper investigates how small shape changes of an obstacle affect the flow of non-Newtonian fluids, providing formulas to optimize obstacle design in fluid dynamics.

Contribution

It derives the shape gradient of a cost function for incompressible power-law fluids, enabling shape optimization of obstacles in fluid flow.

Findings

Derived the shape differentiability of the cost function

Expressed the shape gradient for obstacle shape optimization

Facilitates improved design of obstacles in fluid flows

Abstract

We study the shape differentiability of a cost function for the flow of an incompressible viscous fluid of power-law type. The fluid is confined to a bounded planar domain surrounding an obstacle. For smooth perturbations of the shape of the obstacle we express the shape gradient of the cost function which can be subsequently used to improve the initial design.