A basic model of unconventional gas microscale flow based on the lattice Boltzmann method
ZHAO Yulong,LIU Xiangyu,ZHANG Liehui,SHAN Baochao
Table 1 Relationships between the dimensionless relaxation time and Kn.
Reference Relational expression
Nie et al.[30] $ \tau=1 / 2+K n H \rho / a$
Lim et al.[15] $\tau=\operatorname{Kn} N$
Niu et al.[14] $\tau=\sqrt{6 / \gamma \pi} \mathrm{Kn} \mathrm{H}$
Lee et al.[31] $\tau=1 / 2+K n N$
Tang et al.[33], Zhang et al.[34] $\tau=1 / 2+\sqrt{3 \pi / 8} \operatorname{Kn} N$
Guo et al.[35] $\tau=1 / 2+\sqrt{6 / \pi} \operatorname{Kn} N$
Guo et al.[32] (The influence of Knudsen layer is considered) $\tau=1 / 2+\sqrt{6 / \pi} \operatorname{Kn} N \psi(K n), \psi(K n)=(2 / \pi) \arctan \left(\sqrt{2} K n^{-3 / 4}\right)$
Li et al.[38] (The influence of Knudsen layer is considered) $\tau=1 / 2+\sqrt{6 / \pi} \operatorname{Kn} N \psi(K n), \psi(K n)=1 /(1+2 K n)$
Zhang et al.[40] (The influence of Knudsen layer is considered) $\tau=1 / 2+\sqrt{3 \pi / 8} \operatorname{Kn} N /\left\{1+0.7\left[\mathrm{e}^{-C y / \lambda}+\mathrm{e}^{-C(H-y) / \lambda}\right]\right\}$
Tang et al.[41] (The influence of Knudsen layer is considered) $\tau=1 / 2+\left(\lambda / \lambda_{0}\right) \sqrt{\pi / 8}\left(c / c_{\mathrm{s}}\right) \operatorname{Kn} N$
Guo et al.[42] (The influence of Knudsen layer is considered) $\tau=1 / 2+\sqrt{6 / \pi} K n N\left[1+(y / \lambda-1) \mathrm{e}^{-y / \lambda}-(y / \lambda)^{2} \operatorname{Ei}(y / \lambda)\right]$