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

Wenjing Yan, Axia Wang and Yichen Ma

Mathematical Problems in Engineering, 2013, vol. 2013, 1-11

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:728534

DOI: 10.1155/2013/728534

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