Table 2 Comparison between GSIS-LVDSMC and LVDSMC (values in parentheses) algorithms for the 2D Poiseuille flow in square channel

\({Kn}\)

0.01

0.1

1

10

Number of cells \((N_{x_1}\times N_{x_2})\)

\(50\times 50\)

\(25\times 25\)

(\(100\times 100\))

(\(25\times 25\))

\(N_{x_1}\times {\it{\Delta}} \hat{t}\)

0.1 (1.0)

1.0 (1.0)

Number of time steps in transition state

100

200

800

1000

(\(4\times 10^4\))

(4000)

(1000)

(1000)

Number of time steps in steady state

\(4\times 10^4\)

\(9\times 10^4\)

\(1.3\times 10^5\)

\(1.4\times 10^5\)

(\(5\times 10^5\))

(\(10^5\))

(\(1.3\times 10^5\))

(\(1.4\times 10^5\))

CPU Time

2 h

1700 s

1000 s

1200 s

(108 h)

(2000 s)

(900 s)

(1000 s)

Number of particles

25000

6000

5000

6000

(150000)

(6000)

(5000)

(6000)

Error relative to GSIS-DVM

0.9%

3.26%

0.45%

0.14%

(42%)

(1.24%)

(0.05%)

(0.03%)