The incompressible Navier-Stokes limit from the lattice BGK Boltzmann equation
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917404687204352 |
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| author | Gu, Zhongyang Hu, Xin Matharu, Pritpal Protas, Bartosz Sasada, Makiko Yoneda, Tsuyoshi |
| author_facet | Gu, Zhongyang Hu, Xin Matharu, Pritpal Protas, Bartosz Sasada, Makiko Yoneda, Tsuyoshi |
| contents | In this paper, we prove that a local weak solution to the $d$-dimensional incompressible Navier-Stokes equations ($d \geq 2$) can be constructed by taking the hydrodynamic limit of a velocity-discretized Boltzmann equation with a simplified BGK collision operator. Moreover, in the case when the dimension is $d=2,3$, we characterize the combinations of finitely many particle velocities and probabilities that lead to the incompressible Navier-Stokes equations in the hydrodynamic limit. Numerical computations conducted in 2D provide information about the rate with which this hydrodynamic limit is achieved when the Knudsen number tends to zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20804 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The incompressible Navier-Stokes limit from the lattice BGK Boltzmann equation Gu, Zhongyang Hu, Xin Matharu, Pritpal Protas, Bartosz Sasada, Makiko Yoneda, Tsuyoshi Analysis of PDEs 35Q30, 76D05, 76P05, 76M28 In this paper, we prove that a local weak solution to the $d$-dimensional incompressible Navier-Stokes equations ($d \geq 2$) can be constructed by taking the hydrodynamic limit of a velocity-discretized Boltzmann equation with a simplified BGK collision operator. Moreover, in the case when the dimension is $d=2,3$, we characterize the combinations of finitely many particle velocities and probabilities that lead to the incompressible Navier-Stokes equations in the hydrodynamic limit. Numerical computations conducted in 2D provide information about the rate with which this hydrodynamic limit is achieved when the Knudsen number tends to zero. |
| title | The incompressible Navier-Stokes limit from the lattice BGK Boltzmann equation |
| topic | Analysis of PDEs 35Q30, 76D05, 76P05, 76M28 |
| url | https://arxiv.org/abs/2407.20804 |