TY  - EJOU
AU  - Suga, Kazuhiko 
AU  - Ito, Takahiko 

TI  - Optimization of the Multiple-Relaxation-Time Micro-Flow Lattice Boltzmann Method
T2  - Structural Longevity

PY  - 2011
VL  - 5
IS  - 3
SN  - 1944-6128

AB  - Evaluation and optimization of the multiple-relaxation-time (MRT)
lattice Boltzmann method for micro-flows (µ-flow LBM) are performed with the
two-dimensional nine discrete velocity (D2Q9) model. The MRT µ-flow LBM
consisting of the combination of bounce-back and full diffusive (CBBFD) wall
boundary condition is considered. Based on the discussion of Chai et al. (2010),
the presently applied CBBFD model and relaxation time for heat flux τ<sub>q</sub> satisfy the
second-order slip boundary condition. However, modification to the MRT model
of Chai et al. (MRT-C) is made to the relaxation time for the moments related to
the stress τ<sub>s</sub> by introducing the psi function (Stops,1970; Guo et al., 2006). This
modified MRT-C model (MRT-Cm1) and further modified model (MRT-Cm2) by
changing the coefficients of the second-order slip velocity to the coefficients of Mitsuya (1993) are evaluated. As shown in Fig.1, since the MRT-Cm2 model performs
best among the evaluated models including the one by Verhaeghe et al. (MRT-V) in
predicting slip velocities and flow rates of Poiseuille flows in the range of Knudsen
number 0.01<Kn<10, it is further evaluated in the flow around an obstacle situated
in a nanochannel. Two kinds of obstacles are considered: a square cylinder (Suga
et al., 2010) and a triangular prism. For producing the reference data of the triangular prism flow, the classical molecular dynamics simulation using Lennard-Jones
potential is also performed in the present study. An interpolation scheme is applied
to the CBBBFD wall boundary model for describing the surfaces of the triangular
prism. As shown in Figs.2 and 3, it is confirmed that the MRT-Cm2 model performs
much better than the SRT µ-flow LBM of Niu et al. (2007) (SRT-N).
KW  - lattice Boltzmann method
KW  -  Knudsen number
KW  -  molecular dynamics simulation
KW  -  Poiseuille flow
KW  -  obstacle flow

DO  - 10.3970/sl.2011.005.157