A modified lattice Boltzmann approach based on radial basis function approximation for the non‐uniform rectangular mesh
We have presented a novel lattice Boltzmann approach for the non‐uniform rectangular mesh based on the radial basis function approximation (RBF‐LBM). The non‐uniform rectangular mesh is a good option for local grid refinement, especially for the wall boundaries and flow areas with intensive change o...
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| Vydané v: | International journal for numerical methods in fluids Ročník 96; číslo 11; s. 1695 - 1714 |
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| Hlavní autori: | , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Hoboken, USA
John Wiley & Sons, Inc
01.11.2024
Wiley Subscription Services, Inc |
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| ISSN: | 0271-2091, 1097-0363 |
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| Abstract | We have presented a novel lattice Boltzmann approach for the non‐uniform rectangular mesh based on the radial basis function approximation (RBF‐LBM). The non‐uniform rectangular mesh is a good option for local grid refinement, especially for the wall boundaries and flow areas with intensive change of flow quantities. Which allows, the total number of grid cells to be reduced and so the computational cost, therefore improving the computational efficiency. But the grid structure of the non‐uniform rectangular mesh is no longer applicable to the classic lattice Boltzmann method (CLBM), which is based on the famous BGK collision‐streaming evolution. This is why the present study is inspired by the idea of the interpolation‐supplemented LBM (ISLBM) methodology. The ISLBM algorithm is improved in the present manuscript and developed into a novel LBM approach through the radial basis function approximation instead of the Lagrangian interpolation scheme. The new approach is validated for both steady states and unsteady periodic solutions. The comparison between the radial basis function approximation and the Lagrangian interpolation is discussed. It is found that the novel approach has a good performance on computational accuracy and efficiency. Proving that the non‐uniform rectangular mesh allows grid refinement while obtaining precise flow predictions.
When compared with the classic lattice Boltzmann method, the convergence speed of the present RBF‐LBM is highly accelerated. The modified algorithm is trustable for both steady and unsteady solutions. Numerical results have a good agreement with that of the classic LBM and are more accurate than that of the Lagrangian interpolation schemes. |
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| AbstractList | We have presented a novel lattice Boltzmann approach for the non‐uniform rectangular mesh based on the radial basis function approximation (RBF‐LBM). The non‐uniform rectangular mesh is a good option for local grid refinement, especially for the wall boundaries and flow areas with intensive change of flow quantities. Which allows, the total number of grid cells to be reduced and so the computational cost, therefore improving the computational efficiency. But the grid structure of the non‐uniform rectangular mesh is no longer applicable to the classic lattice Boltzmann method (CLBM), which is based on the famous BGK collision‐streaming evolution. This is why the present study is inspired by the idea of the interpolation‐supplemented LBM (ISLBM) methodology. The ISLBM algorithm is improved in the present manuscript and developed into a novel LBM approach through the radial basis function approximation instead of the Lagrangian interpolation scheme. The new approach is validated for both steady states and unsteady periodic solutions. The comparison between the radial basis function approximation and the Lagrangian interpolation is discussed. It is found that the novel approach has a good performance on computational accuracy and efficiency. Proving that the non‐uniform rectangular mesh allows grid refinement while obtaining precise flow predictions. We have presented a novel lattice Boltzmann approach for the non‐uniform rectangular mesh based on the radial basis function approximation (RBF‐LBM). The non‐uniform rectangular mesh is a good option for local grid refinement, especially for the wall boundaries and flow areas with intensive change of flow quantities. Which allows, the total number of grid cells to be reduced and so the computational cost, therefore improving the computational efficiency. But the grid structure of the non‐uniform rectangular mesh is no longer applicable to the classic lattice Boltzmann method (CLBM), which is based on the famous BGK collision‐streaming evolution. This is why the present study is inspired by the idea of the interpolation‐supplemented LBM (ISLBM) methodology. The ISLBM algorithm is improved in the present manuscript and developed into a novel LBM approach through the radial basis function approximation instead of the Lagrangian interpolation scheme. The new approach is validated for both steady states and unsteady periodic solutions. The comparison between the radial basis function approximation and the Lagrangian interpolation is discussed. It is found that the novel approach has a good performance on computational accuracy and efficiency. Proving that the non‐uniform rectangular mesh allows grid refinement while obtaining precise flow predictions. When compared with the classic lattice Boltzmann method, the convergence speed of the present RBF‐LBM is highly accelerated. The modified algorithm is trustable for both steady and unsteady solutions. Numerical results have a good agreement with that of the classic LBM and are more accurate than that of the Lagrangian interpolation schemes. |
| Author | An, B. Sang, W. M. Hu, X. Li, D. Bergadà, J. M. |
| Author_xml | – sequence: 1 givenname: X. orcidid: 0000-0002-5182-2560 surname: Hu fullname: Hu, X. organization: Northwestern Polytechnical University – sequence: 2 givenname: J. M. surname: Bergadà fullname: Bergadà, J. M. organization: Universitat Politécnica de Catalunya – sequence: 3 givenname: D. surname: Li fullname: Li, D. organization: Northwestern Polytechnical University – sequence: 4 givenname: W. M. surname: Sang fullname: Sang, W. M. organization: Northwestern Polytechnical University – sequence: 5 givenname: B. orcidid: 0000-0001-8738-2504 surname: An fullname: An, B. email: bo_alan_an@163.com organization: The Youth Innovation Team of Shaanxi Universities |
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| Snippet | We have presented a novel lattice Boltzmann approach for the non‐uniform rectangular mesh based on the radial basis function approximation (RBF‐LBM). The... |
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| SubjectTerms | Algorithms Approximation Computational efficiency Computer applications Computing costs Grid refinement (mathematics) Interpolation LBM non‐uniform rectangular mesh Radial basis function radial basis function approximation steady and unsteady solutions Streaming |
| Title | A modified lattice Boltzmann approach based on radial basis function approximation for the non‐uniform rectangular mesh |
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