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Title: Forcing scheme analysis for the axisymmetric lattice Boltzmann method under incompressible limit
Authors: Zhang, Liangqi
Yang, Shiliang
Zeng, Zhong
Chen, Jie
Yin, Linmao
Chew, Jia Wei
Keywords: Centered Schemes
Discrete Lattices
Issue Date: 2017
Source: Zhang, L., Yang, S., Zeng, Z., Chen, J., Yin, L., & Chew, J. W. (2017). Forcing scheme analysis for the axisymmetric lattice Boltzmann method under incompressible limit. Physical Review E, 95(4), 043311-.
Series/Report no.: Physical Review E
Abstract: Because the standard lattice Boltzmann (LB) method is proposed for Cartesian Navier-Stokes (NS) equations, additional source terms are necessary in the axisymmetric LB method for representing the axisymmetric effects. Therefore, the accuracy and applicability of the axisymmetric LB models depend on the forcing schemes adopted for discretization of the source terms. In this study, three forcing schemes, namely, the trapezium rule based scheme, the direct forcing scheme, and the semi-implicit centered scheme, are analyzed theoretically by investigating their derived macroscopic equations in the diffusive scale. Particularly, the finite difference interpretation of the standard LB method is extended to the LB equations with source terms, and then the accuracy of different forcing schemes is evaluated for the axisymmetric LB method. Theoretical analysis indicates that the discrete lattice effects arising from the direct forcing scheme are part of the truncation error terms and thus would not affect the overall accuracy of the standard LB method with general force term (i.e., only the source terms in the momentum equation are considered), but lead to incorrect macroscopic equations for the axisymmetric LB models. On the other hand, the trapezium rule based scheme and the semi-implicit centered scheme both have the advantage of avoiding the discrete lattice effects and recovering the correct macroscopic equations. Numerical tests applied for validating the theoretical analysis show that both the numerical stability and the accuracy of the axisymmetric LB simulations are affected by the direct forcing scheme, which indicate that forcing schemes free of the discrete lattice effects are necessary for the axisymmetric LB method.
ISSN: 1539-3755
DOI: 10.1103/PhysRevE.95.043311
Schools: School of Chemical and Biomedical Engineering 
Research Centres: Nanyang Environment and Water Research Institute 
Singapore Membrane Technology Centre 
Rights: © 2017 American Physical Society (APS). This paper was published in Physical Review E and is made available as an electronic reprint (preprint) with permission of American Physical Society (APS). The published version is available at: []. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.
Fulltext Permission: open
Fulltext Availability: With Fulltext
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