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

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  • Wenjing Yan
  • Axia Wang
  • Yichen Ma

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.

Suggested Citation

  • Wenjing Yan & Axia Wang & Yichen Ma, 2013. "The Application of Shape Gradient for the Incompressible Fluid in Shape Optimization," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-11, April.
    • Handle: RePEc:hin:jnlmpe:728534
    DOI: 10.1155/2013/728534
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