A function space approach to the shape optimization of the Boussinesq system
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917994471358464 |
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| author | Ceretani, Andrea Hu, Weiwei Mu, Lin Rautenberg, Carlos |
| author_facet | Ceretani, Andrea Hu, Weiwei Mu, Lin Rautenberg, Carlos |
| contents | We investigate a shape optimization problem for a heat-conducting fluid governed by a Boussinesq system. The main goal is to determine an optimal domain shape that yields a temperature distribution as uniform as possible. Initially, we analyze the state problem, prove its well-posedness and establish a local boundary regularity result for the weak solution. We then demonstrate the existence of an optimal shape and derive a first-order optimality condition. This requires the derivation and analysis of the adjoint system associated with the Boussinesq model, as well as a rigorous treatment of the directional derivatives of the objective functional under appropriate domain perturbations. Finally, we present numerical experiments that illustrate and support the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15522 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A function space approach to the shape optimization of the Boussinesq system Ceretani, Andrea Hu, Weiwei Mu, Lin Rautenberg, Carlos Analysis of PDEs Optimization and Control We investigate a shape optimization problem for a heat-conducting fluid governed by a Boussinesq system. The main goal is to determine an optimal domain shape that yields a temperature distribution as uniform as possible. Initially, we analyze the state problem, prove its well-posedness and establish a local boundary regularity result for the weak solution. We then demonstrate the existence of an optimal shape and derive a first-order optimality condition. This requires the derivation and analysis of the adjoint system associated with the Boussinesq model, as well as a rigorous treatment of the directional derivatives of the objective functional under appropriate domain perturbations. Finally, we present numerical experiments that illustrate and support the theoretical findings. |
| title | A function space approach to the shape optimization of the Boussinesq system |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2504.15522 |