Comment on “Heat transfer and fluid flow in microchannels and nanochannels at high Knudsen number using thermal lattice-Boltzmann method”

Abstract

In this Comment we reveal the falsehood of the claim that the lattice Bhatnagar-Gross-Krook (BGK) model "is capable of modeling shear-driven, pressure-driven, and mixed shear-pressure-driven rarified [sic] flows and heat transfer up to Kn=1 in the transitional regime" made in a recent paper [Ghazanfarian and Abbassi, Phys. Rev. E 82, 026307 (2010)]. In particular, we demonstrate that the so-called "Knudsen effects" described are merely numerical artifacts of the lattice BGK model and they are unphysical. Specifically, we show that the erroneous results for the pressure-driven flow in a microchannel imply the false and unphysical condition that 6σKn<-1, where Kn is the Knudsen number σ=(2-σ(v))/σ(v) and σ(v)∈(0,1] is the tangential momentum accommodation coefficient. We also show explicitly that the defects of the lattice BGK model can be completely removed by using the multiple-relaxation-time collision model.

Reply to “Comment on ‘Heat transfer and fluid flow in microchannels and nanochannels at high Knudsen number using thermal lattice-Boltzmann method”’

“…L.S.L. [1] points out that our results are erroneous and our claim of "capability of the lattice Boltzmann method to model shear-driven, pressure-driven, and mixed shearpressure-driven rarefied flows and heat transfer up to Kn = 1 in the transitional regime" is false and our results are erroneous. He states that the lattice Bhatnagar-Gross-Krook (LBGK) model with the bounce-back type of boundary conditions is just an incompressible Navier-Stokes solver and is not valid beyond the slip-flow regime.…”

Lattice Boltzmann methods for complex micro-flows: applicability and limitations for practical applications

“…With this in mind, when one wants to discuss the applicability of the models in the µ-flow LBMs for engineering simulations, it is readily understood that a model evaluation only in canonical flows is not sufficient. Therefore, the present author's group extensively tested the µ-flow LBMs in micro/nano obstacle flows to confirm their validity by comparing with the data obtained by performing molecular dynamics (MD) simulations (Koplik andBanavar 1995, Haile 1997, etc) of the Lennard-Jones fluid (Suga et al 2010a, 2010b, 2011, Suga and Ito 2010, 2011. According to those studies, this paper summarizes studies to confirm the applicability and the limitations of the µ-flow LBMs in complex flows for practical applications.…”

“…(For details, see Suga et al 2010a, 2010b, 2011, Suga and Ito 2010, 2011 In the LBM simulations, the reference Knudsen numbers are explicitly given to determine the relaxation time as τ = 1/2 + √ 2/πKnH/(c s δt). obtain the discrete velocity values.…”

“…) Although most of the µ-flow LBM studies were based on the single relaxationtime lattice BGK (LBGK) model, there have been arguments about the applicability of the LBGK model to the micro-flows. For example, Luo (2004Luo ( , 2011 argued that the slip velocities predicted by the LBGK model were merely numerical artifacts. (In the Appendix, the discussions on this issue are developed.)…”

The lattice Boltzmann method for isothermal micro-gaseous flow and its application in shale gas flow: A review

“…It is noteworthy that the LBM was initially extended for simulation of gaseous flows in slip flow regime [50][51][52][53][54][55][56][57]. Advances of the LBM have allowed us to simulate fluid flow in single capillary in transition flow regime [58][59][60][61][62] [66] argued that slip velocity predicted by SRT is merely an artefact at the solid boundaries. For this reason, other LB models, such as two relaxation times (TRT) [67] [68], multiple relaxation times (MRT) [59][61] and Filter-matrix lattice Boltzmann(FMLB) [60] were proposed.…”