Shape optimization in the Navier-Stokes flow with thermal effects

Authors

  • Wenjing Yan,

    Corresponding author
    1. School of Mathematics and Statistics, Xi'an Jiaotong University, Shaanxi 710049, People's Republic of China
    2. Center for Computational Geosciences, Xi'an Jiaotong University, Shaanxi 710049, People's Republic of China
    • Correspondence to: Wenjing Yan; School of Mathematics and Statistics, Xi'an Jiaotong University, Shaanxi 710049, People's Republic of China wenjingyan@mail.xjtu.edu.cn)

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  • Zhiming Gao

    1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, People'sRepublic of China
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Abstract

In this article, we consider the shape optimization problem of a body immersed in the incompressible fluid governed by Navier-Stokes equations coupling with a thermal model. Based on the continuous adjoint method, we formulate and analyze the shape optimization problem. Then we derive the structure of shape gradient for the cost functional by using the differentiability of a minimax formulation involving a Lagrange functional with the function space parametrization technique. Moreover, we present a gradient-type algorithm to the shape optimization problem. Finally, numerical examples demonstrate the feasibility and effectiveness of the proposed algorithm. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1700–1715, 2014

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