The Application of Shape Gradient for the Incompressible Fluid in Shape Optimization

Abstract EN

This paper is concerned with the numerical simulation for shape optimization of the Stokes flow around a solid body.

The shape gradient for the shape optimization problem in a viscous incompressible flow is evaluated by the velocity method.

The flow is governed by the steady-state Stokes equations coupled with a thermal model.

The structure of continuous shape gradient of the cost functional is derived by employing the differentiability of a minimax formulation involving a Lagrange functional with the function space parametrization technique.

A gradient-type algorithm is applied to the shape optimization problem.

Numerical examples show that our theory is useful for practical purpose, and the proposed algorithm is feasible and effective.