Energy stable gradient flow schemes for shape and topology optimization in Navier-Stokes flows
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910438809141248 |
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| author | Li, Jiajie Zhu, Shengfeng |
| author_facet | Li, Jiajie Zhu, Shengfeng |
| contents | We study topology optimization governed by the incompressible Navier-Stokes flows using a phase field model. Novel stabilized semi-implicit schemes for the gradient flows of Allen-Cahn and Cahn-Hilliard types are proposed for solving the resulting optimal control problem. Unconditional energy stability is shown for the gradient flow schemes in continuous and discrete spaces. Numerical experiments of computational fluid dynamics in 2d and 3d show the effectiveness and robustness of the optimization algorithms proposed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_05098 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Energy stable gradient flow schemes for shape and topology optimization in Navier-Stokes flows Li, Jiajie Zhu, Shengfeng Numerical Analysis Optimization and Control Fluid Dynamics 49Q10 49Q12 76D55 76M10 We study topology optimization governed by the incompressible Navier-Stokes flows using a phase field model. Novel stabilized semi-implicit schemes for the gradient flows of Allen-Cahn and Cahn-Hilliard types are proposed for solving the resulting optimal control problem. Unconditional energy stability is shown for the gradient flow schemes in continuous and discrete spaces. Numerical experiments of computational fluid dynamics in 2d and 3d show the effectiveness and robustness of the optimization algorithms proposed. |
| title | Energy stable gradient flow schemes for shape and topology optimization in Navier-Stokes flows |
| topic | Numerical Analysis Optimization and Control Fluid Dynamics 49Q10 49Q12 76D55 76M10 |
| url | https://arxiv.org/abs/2405.05098 |