Consistent multiple-relaxation-time lattice Boltzmann method for the volume averaged Navier-Stokes equations
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914380308807680 |
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| author | Liu, Yang Zhang, Xuan Min, Jingchun Wu, Xiaomin |
| author_facet | Liu, Yang Zhang, Xuan Min, Jingchun Wu, Xiaomin |
| contents | Recently, we notice that a pressure-based lattice Boltzmann (LB) method was established to recover the volume-averaged Navier-Stokes equations (VANSE), which serve as the cornerstone of various fluid-solid multiphase models. It decouples the pressure from density and exhibits excellent numerical performance, however, the widely adopted density-based LB scheme still suffers from significant spurious velocities and inconsistency with VANSE. To remedy this issue, a multiple-relaxation-time LB method is devised in this work, which incorporates a provisional equation of state in an adjusted density equilibrium distribution to decouple the void fraction from density. The Galilean invariance of the recovered VANSE is guaranteed by introducing a penalty source term in moment space, effectively eliminating unwanted numerical errors. Through the Chapman-Enskog analysis and detailed numerical validations, this novel method is proved to be capable of recovering VANSE with second-order accuracy consistently, and well-suited for handling void fraction fields with large gradients and spatiotemporal distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Consistent multiple-relaxation-time lattice Boltzmann method for the volume averaged Navier-Stokes equations Liu, Yang Zhang, Xuan Min, Jingchun Wu, Xiaomin Fluid Dynamics Numerical Analysis Recently, we notice that a pressure-based lattice Boltzmann (LB) method was established to recover the volume-averaged Navier-Stokes equations (VANSE), which serve as the cornerstone of various fluid-solid multiphase models. It decouples the pressure from density and exhibits excellent numerical performance, however, the widely adopted density-based LB scheme still suffers from significant spurious velocities and inconsistency with VANSE. To remedy this issue, a multiple-relaxation-time LB method is devised in this work, which incorporates a provisional equation of state in an adjusted density equilibrium distribution to decouple the void fraction from density. The Galilean invariance of the recovered VANSE is guaranteed by introducing a penalty source term in moment space, effectively eliminating unwanted numerical errors. Through the Chapman-Enskog analysis and detailed numerical validations, this novel method is proved to be capable of recovering VANSE with second-order accuracy consistently, and well-suited for handling void fraction fields with large gradients and spatiotemporal distributions. |
| title | Consistent multiple-relaxation-time lattice Boltzmann method for the volume averaged Navier-Stokes equations |
| topic | Fluid Dynamics Numerical Analysis |
| url | https://arxiv.org/abs/2409.02964 |