Relationship between accuracy and number of velocity particles in velocity slip phenomena was investigated by numerical simulations and theoretical considerations. Two types of 2D models were used: the octagon family and the D2Q9 model. Models have to possess the following four prerequisites to accurately simulate the velocity slip phenomena: (a) equivalency to the Navier–Stokes equations in the N-S flow area, (b) conservation of momentum flow $Pxy$ in the whole area, (c) appropriate relaxation process in the Knudsen layer, and (d) capability to properly express the mass and momentum flows on the wall. Both the octagon family and the D2Q9 model satisfy conditions (a) and (b). However, models with fewer velocity particles do not sufficiently satisfy conditions (c) and (d). The D2Q9 model fails to represent a relaxation process in the Knudsen layer and shows a considerable fluctuation in the velocity slip due to the model’s angle to the wall. To perform an accurate velocity slip simulation, models with sufficient velocity particles, such as the triple octagon model with moving particles of 24 directions, are desirable.

1.
Lim
,
C. Y.
,
Shu
,
C.
,
Niu
,
X. D.
, and
Chew
,
Y. T.
, 2002, “
Application of Lattice Boltzmann Method to Simulate Microchannel Flows
,”
Phys. Fluids
1070-6631,
14
(
7
), pp.
2299
2308
.
2.
Nie
,
X.
,
Doolen
,
G. D.
, and
Chen
,
S.
, 2002, “
Lattice-Boltzmann Simulations of Fluid Flows in MEMS
,”
J. Stat. Phys.
0022-4715,
107
, pp.
279
289
.
3.
Ansumali
,
S.
, and
Karlin
,
I. V.
, 2002, “
Kinetic Boundary Conditions in the Lattice Boltzmann Method
,”
Phys. Rev. E
1063-651X,
66
, p.
026311
.
4.
Sbragaglia
,
M.
, and
Succi
,
S.
, 2005, “
Analytical Calculation of Slip Flow in Lattice Boltzmann Models With Kinetic Boundary Conditions
,”
Phys. Fluids
1070-6631,
17
, p.
093602
.
5.
Tang
,
G. H.
,
Tao
,
W. Q.
, and
He
,
Y. L.
, 2005, “
Lattice Boltzmann Method for Gaseous Microflows Using Kinetic Theory Boundary Conditions
,”
Phys. Fluids
1070-6631,
17
, p.
058101
.
6.
Zhang
,
Y.
,
Qin
,
R.
, and
Emerson
,
D. R.
, 2005, “
Lattice Boltzmann Simulation of Rarefied Gas Flows in Microchannels
,”
Phys. Rev. E
1063-651X,
71
, p.
047702
.
7.
Sofonea
,
V.
, and
Sekerka
,
R. F.
, 2005, “
Diffuse-Reflection Boundary Conditions for a Thermal Lattice Boltzmann Model in Two Dimensions: Evidence of Temperature Jump And Slip Velocity in Microchannels
,”
Phys. Rev. E
1063-651X,
71
, p.
066709
.
8.
Sofonea
,
V.
, and
Sekerka
,
R. F.
, 2005, “
Boundary Conditions for the Upwind Finite Difference Lattice Boltzmann Model: Evidence of Slip Velocity in Micro-Channel Flow
,”
J. Comput. Phys.
0021-9991,
207
, pp.
639
659
.
9.
Niu
,
X. D.
,
Hyodo
,
S. A.
,
Munekata
,
T.
, and
Suga
,
K.
, 2007, “
Kinetic Lattice Boltzmann Method for Microscale Gas Flows: Issues on Boundary Condition, Relaxation Time, and Regularization
,”
Phys. Rev. E
1063-651X,
76
, p.
036711
.
10.
Zhang
,
R.
,
Shan
,
X.
, and
Chen
,
H.
, 2006, “
Efficient Kinetic Method for Fluid Simulation Beyond the Navier-Stokes Equation
,”
Phys. Rev. E
1063-651X,
74
, p.
046703
.
11.
Guo
,
Z.
,
Zheng
,
C.
, and
Shi
,
B.
, 2008, “
Lattice Boltzmann Equation With Multiple Effective Relaxation Times for Gaseous Microscale Flow
,”
Phys. Rev. E
1063-651X,
77
, p.
036707
.
12.
Chen
,
Y.
,
Ohashi
,
H.
, and
Akiyama
,
M.
, 1994, “
Thermal Lattice Bhatnagar-Gross-Krook Model Without Nonlinear Deviations in Macrodynamic Equations
,”
Phys. Rev. E
1063-651X,
50
, pp.
2776
2783
.
13.
Watari
,
M.
, and
Tsutahara
,
M.
, 2004, “
Possibility of Constructing a Multispeed Bhatnagar-Gross-Krook Thermal Model of the Lattice Boltzmann Method
,”
Phys. Rev. E
1063-651X,
70
, p.
016703
.
14.
Watari
,
M.
, 2009, “
Velocity Slip and Temperature Jump Simulations by the Three-Dimensional Thermal Finite-Difference Lattice Boltzmann Method
,”
Phys. Rev. E
1063-651X,
79
, p.
066706
.
15.
Watari
,
M.
, and
Tsutahara
,
M.
, 2006, “
Supersonic Flow Simulations by a Three-Dimensional Multispeed Thermal Model of the Finite Difference Lattice Boltzmann Method
,”
Physica A
0378-4371,
364
, pp.
129
144
.
16.
Watari
,
M.
, and
Tsutahara
,
M.
, 2003, “
Two-Dimensional Thermal Model of the Finite-Difference Lattice Boltzmann Method With High Spatial Isotropy
,”
Phys. Rev. E
1063-651X,
67
, p.
036306
.
17.
Qian
,
Y. H.
,
D’Humieres
,
D.
, and
Lallemand
,
P.
, 1992, “
Lattice BGK Models for Navier-Stokes Equation
,”
Europhys. Lett.
0295-5075,
17
(
6
), pp.
479
484
.
18.
Maxwell
,
J. C.
, 1879, “
On Stresses in Rarefied Gases Arising From Inequalities of Temperature
,”
Philos. Trans. R. Soc. London
0962-8428,
170
, pp.
231
256
.
19.
Kennard
,
E. H.
, 1938,
Kinetic Theory of Gases
,
McGraw-Hill
,
New York
.
20.
Albertoni
,
S.
,
Cercignani
,
C.
, and
Gotusso
,
L.
, 1963, “
Numerical Evaluation of the Slip Coefficient
,”
Phys. Fluids
1070-6631,
6
, pp.
993
996
.
21.
Sone
,
Y.
, 1964, “
Kinetic Theory Analysis of Linearized Rayleigh Problem
,”
J. Phys. Soc. Jpn.
0031-9015,
19
(
8
), pp.
1463
1473
.
22.
,
K.
, and
Sone
,
Y.
, 1966, “
Some Studies on Rarefied Gas Flows
,”
J. Phys. Soc. Jpn.
0031-9015,
21
(
7
), pp.
1439
1445
.
23.
Sone
,
Y.
, 1969, “
Asymptotic Theory of Flow of Rarefied Gas Over a Smooth Boundary I
,”
Rarefied Gas Dynamics
,
L.
Trilling
and
H. Y.
Wachman
, eds.,
,
New York
, pp.
243
253
.
24.
Sone
,
Y.
, 1966, “
Some Remarks on Knudsen Layer
,”
J. Phys. Soc. Jpn.
0031-9015,
21
, pp.
1620
1621
.
25.
Onishi
,
Y.
, 1974, “
Effects of Accommodation Coefficient on Shear Flow of Rarefied Gas
,”
Trans. Jpn. Soc. Aeronaut. Space Sci.
0549-3811,
17
, pp.
93
98
.
26.
Sone
,
Y.
, and
Aoki
,
K.
, 1994,
Molecular Gas Dynamics
,
Asakura
,
Tokyo
, in Japanese.
27.
Aoki
,
K.
, 2001, “
Dynamics of Rarefied Gas Flows: Asymptotic and Numerical Analyses of the Boltzmann Equation
,”
39th AIAA Aerospace Sciences Meeting and Exhibit
, Reno, NV, Jan. 8–11, AIAA Paper No. 2001-0874.
28.
Sone
,
Y.
, 2002,
Kinetic Theory and Fluid Dynamics
,
Birkhäuser
,
Boston
.
29.
,
H.
, 1963,
Differential Equations: A Modern Approach
,
Holt, Rinehart and Winston
,
New York
.
30.
,
T.
,
Sone
,
Y.
, and
Aoki
,
K.
, 1989, “
Numerical Analysis of the Shear and Thermal Creep Flows on a Rarefied Gas Over a Plane Wall on the Basis of the Linearized Boltzmann Equation for Hard-Sphere Molecules
,”
Phys. Fluids A
0899-8213,
1
(
9
), pp.
1588
1599
.
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