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Numerical Analysis of the Lattice Boltzmann Method for the Boussinesq Equations

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Abstract

This paper is concerned with the lattice Boltzmann method (LBM) with BGK collision models for the two-dimensional Bousinessq equations on periodic domains. We show the numerical stability of the LBM linearized at a quiescent state and conduct a formal asymptotic analysis which indicates the consistency of the method to the Boussinesq equations. With these, we establish the convergence of the LBM for the nonlinear equations. Moreover, our present analysis provides some important hints on how to construct initial data and how to add force terms in the LBM. It can be straightforwardly extended to other LB models or three-dimensional cases.

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Acknowledgements

This work was partially supported by the Sino-German Research Group Project (No. GZ 1465) and the National Natural Science Foundation of China (Nos. 11471185, 11801030, 11861131004).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China

    Wen-An Yong

  2. Department of Applied Mathematics, University of Science and Technology Beijing, Beijing, 100083, People’s Republic of China

    Weifeng Zhao

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  1. Wen-An Yong
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  2. Weifeng Zhao
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Correspondence to Weifeng Zhao.

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Yong, WA., Zhao, W. Numerical Analysis of the Lattice Boltzmann Method for the Boussinesq Equations. J Sci Comput 84, 36 (2020). https://doi.org/10.1007/s10915-020-01291-0

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  • DOI: https://doi.org/10.1007/s10915-020-01291-0

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