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Topology optimization of steady Navier-Stokes flow via a piecewise constant level set method

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Abstract

This paper presents a piecewise constant level set method for the topology optimization of steady Navier-Stokes flow. Combining piecewise constant level set functions and artificial friction force, the optimization problem is formulated and analyzed based on a design variable. The topology sensitivities are computed by the adjoint method based on Lagrangian multipliers. In the optimization procedure, the piecewise constant level set function is updated by a new descent method, without the needing to solve the Hamilton-Jacobi equation. To achieve optimization, the piecewise constant level set method does not track the boundaries between the different materials but instead through the regional division, which can easily create small holes without topological derivatives. Furthermore, we make some attempts to avoid updating the Lagrangian multipliers and to deal with the constraints easily. The algorithm is very simple to implement, and it is possible to obtain the optimal solution by iterating a few steps. Several numerical examples for both two- and three-dimensional problems are provided, to demonstrate the validity and efficiency of the proposed method.

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Acknowledgements

This research is supported by Zhejiang University City College Scientific Research Foundation (JZD17001). The authors would like to thank the editor and referees for their valuable comments and suggestions that help us to improve this paper.

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Authors and Affiliations

  1. School of Computing Science, Zhejiang University City College, Hangzhou, 310015, Zhejiang, People’s Republic of China

    Xiaoxia Dai & Chengwei Zhang

  2. Department of Mathematics, School of Science and Technology, Örebro University, Örebro, 70182, Sweden

    Ye Zhang & Mårten Gulliksson

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  1. Xiaoxia Dai
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  2. Chengwei Zhang
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  3. Ye Zhang
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  4. Mårten Gulliksson
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Correspondence to Chengwei Zhang.

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Dai, X., Zhang, C., Zhang, Y. et al. Topology optimization of steady Navier-Stokes flow via a piecewise constant level set method. Struct Multidisc Optim 57, 2193–2203 (2018). https://doi.org/10.1007/s00158-017-1850-x

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  • DOI: https://doi.org/10.1007/s00158-017-1850-x

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