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Finite volume scheme for the lattice Boltzmann method on curved surfaces in 3D

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Abstract

The fluid flows on the surface widely exist in the natural world, such as the atmospherical circulation on a planet. In this study, we present a finite volume lattice Boltzmann method (LBM) for simulating fluid flows on curved surfaces in three-dimensional (3D) space. The curved surfaces are discretized using unstructured triangular meshes. We choose the D3Q19 lattice and the triangular meshes for the velocity and spatial discretizations, respectively. In one time iteration, we only need to compute the distribution functions on each vertex in a fully explicit form. Therefore, our proposed method is highly efficient for solving fluid flows on curved surfaces using LBM. To keep the velocity field tangential to the surfaces, a practical velocity correction technique is adopted. We perform a series of computational experiments on various curved surfaces such as sphere, torus, and bunny to demonstrate the performance of the proposed method.

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Acknowledgements

The work of Z. Tan is supported by the National Nature Science Foundation of China (11971502), and Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University (2020B1212060032). S.K. Kim was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2022R1C1C2005275). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2022R1A2C1003844). The authors would like to thank the reviewers for their valuable suggestions and comments to improve the paper.

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Authors and Affiliations

  1. School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, 510275, China

    Junxiang Yang & Zhijun Tan

  2. Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, 510275, China

    Zhijun Tan

  3. Department of Mathematics, Korea University, Seoul, 02841, Republic of Korea

    Sangkwon Kim, Chaeyoung Lee, Soobin Kwak & Junseok Kim

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  1. Junxiang Yang
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Correspondence to Junseok Kim.

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Yang, J., Tan, Z., Kim, S. et al. Finite volume scheme for the lattice Boltzmann method on curved surfaces in 3D. Engineering with Computers 38, 5507–5518 (2022). https://doi.org/10.1007/s00366-022-01671-0

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