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Accuracy of high-order lattice Boltzmann method for non-equilibrium gas flow

Published online by Cambridge University Press:  25 November 2020

Yangyang Shi Open the ORCID record for Yangyang Shi [Opens in a new window] ,
Lei Wu Open the ORCID record for Lei Wu [Opens in a new window]  and
Xiaowen Shan Open the ORCID record for Xiaowen Shan [Opens in a new window]
Yangyang Shi
Affiliation:
School of Astronautics, Harbin Institute of Technology, Harbin, Heilongjiang150001, PR China Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen, Guangdong518055, PR China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong518055, PR China
Lei Wu
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong518055, PR China
Xiaowen Shan*
Affiliation:
Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen, Guangdong518055, PR China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong518055, PR China
*
†Email address for correspondence: shanxw@sustech.edu.cn
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Abstract

The lattice Boltzmann method (LBM), which was originally designed for near-incompressible Navier–Stokes flows, has been extended to rarefied gas flows with high-order quadrature in recent years. Although the ability of the high-order LBM to capture rarefaction effects has been demonstrated by many authors, its accuracy and efficiency are often undermined by numerical dissipation introduced by the off-lattice abscissas in Gauss–Hermite quadrature. Here, using the spontaneous Rayleigh–Brillouin scattering problem as the benchmark, we assess the accuracy and efficiency of the high-order LBM with on-lattice quadrature rules up to 39th order. The numerical error comprises two parts, one due to the rarefaction effect and the other due to temporal-spatial discretization, and we find that the former depends not only on the number of discrete velocities, but also on their distribution in velocity space. With a quadrature of 29th order, the error between the LBM and the discrete velocity method is found to be below 1 % up to $Kn=2.0$. Compared with a finite-volume Bhatnagar–Gross–Krook solver using Gauss–Hermite quadrature, the on-lattice LBM has a numerical dissipation several orders of magnitude lower, and achieves the same accuracy with fewer discrete velocities.

JFM classification

Rarefied Gas Flow: Rarefied Gas Flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 907 , 25 January 2021 , A25
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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