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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.15575 |
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| _version_ | 1866910710513008640 |
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| author | Huang, Qian Rohde, Christian Yong, Wen-An Zhang, Ruixi |
| author_facet | Huang, Qian Rohde, Christian Yong, Wen-An Zhang, Ruixi |
| contents | We introduce a new hyperbolic approximation to the incompressible Navier-Stokes equations by incorporating a first-order relaxation and using the artificial compressibility method. With two relaxation parameters in the model, we rigorously prove the asymptotic limit of the system towards the incompressible Navier-Stokes equations as both parameters tend to zero. Notably, the convergence of the approximate pressure variable is achieved by the help of a linear `auxiliary' system and energy-type error estimates of its differences with the two-parameter model and the Navier-Stokes equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15575 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A hyperbolic relaxation system of the incompressible Navier-Stokes equations with artificial compressibility Huang, Qian Rohde, Christian Yong, Wen-An Zhang, Ruixi Analysis of PDEs 35Q30, 76D05 We introduce a new hyperbolic approximation to the incompressible Navier-Stokes equations by incorporating a first-order relaxation and using the artificial compressibility method. With two relaxation parameters in the model, we rigorously prove the asymptotic limit of the system towards the incompressible Navier-Stokes equations as both parameters tend to zero. Notably, the convergence of the approximate pressure variable is achieved by the help of a linear `auxiliary' system and energy-type error estimates of its differences with the two-parameter model and the Navier-Stokes equations. |
| title | A hyperbolic relaxation system of the incompressible Navier-Stokes equations with artificial compressibility |
| topic | Analysis of PDEs 35Q30, 76D05 |
| url | https://arxiv.org/abs/2411.15575 |