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Assessment of algorithms for the no‐slip boundary condition in the lattice Boltzmann equation of BGK model
Author(s) -
Suh Yong Kweon,
Kang Jinfen,
Kang Sangmo
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1801
Subject(s) - mathematics , lattice boltzmann methods , extrapolation , couette flow , slip (aerodynamics) , boundary value problem , boltzmann equation , quartic function , mathematical analysis , algorithm , geometry , physics , flow (mathematics) , mechanics , pure mathematics , quantum mechanics , thermodynamics
Three kinds of algorithms for the lattice Boltzmann equation of the BGK model in the implementation of the no‐slip boundary condition on the wall are assessed by using the analytical formula for the slip velocity of the fully developed pressure‐driven channel flow. It is shown that the bounce‐back algorithm results in the spatial accuracy of 1st order, except for the case when the wall is located at half way between the two grid lines. The interpolation scheme proposed by Yu et al . ( Prog. Aerospace Sci . 2003; 39 :329–367) and the similar one by Bouzidi et al . ( Phys. Fluids 2001; 13 (11):3452–3459) are of 2nd order, but the error increases quadratically with the relaxation time. The extrapolation scheme of Guo et al . ( Phys. Fluids 2002; 14 (6):2007–2010) is also shown to be of 2nd order, and the error level increases linearly with the relaxation time, but it turns out that this scheme is unstable for a certain range of parameter values. Numerical experiments with various parameter sets have been performed to obtain the stability diagram. Three algorithms are then applied to a circular‐Couette flow and their performance is also studied in terms of the numerical accuracy and stability. Copyright © 2008 John Wiley & Sons, Ltd.