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A new curved boundary treatment in lattice Boltzmann method is developed for micro gas flow in the slip regime. The proposed treatment is a combination of the nonequilibrium extrapolation scheme for curved boundary with no-slip velocity condition and the counter-extrapolation method for the velocity and its normal gradient on the curved boundary. Taking into consideration the effect of the offset between the physical boundary and the closest grid line, the new treatment is proved to be more accurate than the traditional half-way diffusive bounce-back (DBB) scheme. The present treatment is also more applicable than the modified DBB scheme because the specific gas-wall interaction parameters need to be determined to ensure the validation of the modified DBB scheme.The proposed boundary treatment is implemented to simulate the benchmark problems, which include a Poiseuille flow in the aligned/inclined micro-channel, a flow past a microcylinder and a microcylindrical Couette flow. The results and conclusions are summarized as follows.1) The force-driven Poiseuille flow in an aligned microchannel is simulated separately with different values of wall-grid offset qδx (q=0.25, 0.5, 0.75, 1.0). With the consideration of the wall-grid offset, the numerical results with the new boundary treatment show good agreement with the analytical solutions. However, the results obtained by using the half-way DBB scheme only accord well with the analytical solutions under the condition of a fixed wall-grid offset (q=0.5).2) To demonstrate the capability of the present treatment in dealing with gas flow in a more complex geometry, the force-driven Poiseuille flow in a micro-channel is investigated separately with different inclined angles. The present numerical results fit well with the analytical solutions. However, the discrepancy between the results obtained with the half-way DBB scheme and the analytical solutions can be clearly observed near the inclined boundaries.3) The gas flow past a microcylinder is simulated to prove that the present treatment can deal with the curved boundary. The slip velocity profile along the micro cylinder periphery obtained with the present treatment accords well with the available data in the published literature. However, the results obtained with the half-way DBB scheme show lower values than the results from the published work.4) In the simulations of the microcylindrical Couette flow between two coaxial rotating cylinders for different Knudsen numbers the results obtained by using the present treatment show excellent agreement with the analytical solutions. However, the results obtained with the half-way DBB scheme and the modified DBB scheme deviate obviously from the analytical solutions near the inner and outer cylindrical walls, respectively.In summary, the new boundary treatment proposed in this work is capable of dealing with the complex gas-solid boundary in the slip regime. The new treatment has a higher accuracy than the half-way DBB scheme and shows a better applicability than the modified DBB scheme.
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Keywords:
- curved boundary /
- lattice Boltzmann method /
- slip regime /
- micro gas flow
[1] Gad-el-Hak M 1999 ASME J. Fluids Eng. 121 5
[2] Ho C M, Tai Y C 1998 Annu. Rev. Fluid Mech. 30 579
[3] Zhang T T, Jia L, Wang Z C 2008 Chin. Phys. Lett. 25 180
[4] Sun X M, He F, Ding Y T 2003 Chin. Phys. Lett. 20 2199
[5] Liu C F, Ni Y S 2008 Chin. Phys. B 17 4554
[6] Tao S, Wang L, Guo Z L 2014 Acta Phys. Sin. 63 214703 (in Chinese) [陶实, 王亮, 郭照立 2014 物理学报 63 214703]
[7] Wang Z, Liu Y, Zhang J Z 2016 Acta Phys. Sin. 65 014703 (in Chinese) [王佐, 刘雁, 张家忠 2016 物理学报 65 014703]
[8] Guo Z L, Zheng C G, Shi B C 2002 Phys. Fluids 14 2007
[9] Mei R W, Luo L S, Shyy W 1999 J. Comput. Phys. 155 307
[10] Ladd A J C 1994 J. Fluid Mech. 271 285
[11] Noble D R, Torczynski J R 1998 Int. J. Mod. Phys. C 9 1189
[12] Yu Z, Yang H, Fan L S 2011 Chem. Eng. Sci. 66 3441
[13] Lee C H, Huang Z H, Chiew Y M 2015 Eng. Appl. Comp. Fluid 9 370
[14] Guo K K, Li L K, Xiao G, AuYeung N A, Mei R W 2015 Int. J. Heat Mass Tran. 88 306
[15] Yin X W, Zhang J F 2012 J. Comput. Phys. 231 4295
[16] Shi D Y, Wang Z K, Zhang A M 2014 Acta Phys. Sin. 63 074703 (in Chinese) [史冬岩, 王志凯, 张阿漫 2014 物理学报 63 074703]
[17] Le G G, Oulaid O, Zhang J F 2015 Phys. Rev. E 91 033306
[18] Fu S C, Leung W W F, So R M C 2013 Commun. Comput. Phys. 14 126
[19] Gao D Y, Chen Z Q, Chen L H, Zhang D L 2017 Int. J. Heat Mass Tran. 105 673
[20] Izham M, Fukui T, Morinishi K 2011 J. Fluid Sci. Tech. 6 812
[21] Nie D M, Lin J Z 2010 Chin. Phys. Lett. 27 104701
[22] Fang H P, Wan R Z, Fan L W 2000 Chin. Phys. 9 515
[23] Szalmas L 2007 Int. J. Mod. Phys. C 18 15
[24] Tao S, Guo Z L 2015 Phys. Rev. E 91 043305
[25] Guo Z L, Shi B C, Zheng C G 2011 Comput. Math. Appl. 61 3519
[26] Suga K 2013 Fluid Dyn. Res. 45 034501
[27] Yang W L, Li H X, Zhang T J, Elfadel I M 2015 ASME 2015 13th International Conference on Nanochannels, Microchannels, and Minichannels San Francisco, CA, USA, July 6-9, 2015 pV001T04A001
[28] Buick J M, Greated C A 2000 Phys. Rev. E 61 5307
[29] Guo Z L, Zheng C G, Shi B C 2002 Phys. Rev. E 65 046308
[30] Sun Y H, Barber R W, Emerson D R 2005 Phys. Fluids 17 047102
[31] Beskok A, Karniadakis G E 1994 J. Thermophys. Heat Tr. 8 647
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[1] Gad-el-Hak M 1999 ASME J. Fluids Eng. 121 5
[2] Ho C M, Tai Y C 1998 Annu. Rev. Fluid Mech. 30 579
[3] Zhang T T, Jia L, Wang Z C 2008 Chin. Phys. Lett. 25 180
[4] Sun X M, He F, Ding Y T 2003 Chin. Phys. Lett. 20 2199
[5] Liu C F, Ni Y S 2008 Chin. Phys. B 17 4554
[6] Tao S, Wang L, Guo Z L 2014 Acta Phys. Sin. 63 214703 (in Chinese) [陶实, 王亮, 郭照立 2014 物理学报 63 214703]
[7] Wang Z, Liu Y, Zhang J Z 2016 Acta Phys. Sin. 65 014703 (in Chinese) [王佐, 刘雁, 张家忠 2016 物理学报 65 014703]
[8] Guo Z L, Zheng C G, Shi B C 2002 Phys. Fluids 14 2007
[9] Mei R W, Luo L S, Shyy W 1999 J. Comput. Phys. 155 307
[10] Ladd A J C 1994 J. Fluid Mech. 271 285
[11] Noble D R, Torczynski J R 1998 Int. J. Mod. Phys. C 9 1189
[12] Yu Z, Yang H, Fan L S 2011 Chem. Eng. Sci. 66 3441
[13] Lee C H, Huang Z H, Chiew Y M 2015 Eng. Appl. Comp. Fluid 9 370
[14] Guo K K, Li L K, Xiao G, AuYeung N A, Mei R W 2015 Int. J. Heat Mass Tran. 88 306
[15] Yin X W, Zhang J F 2012 J. Comput. Phys. 231 4295
[16] Shi D Y, Wang Z K, Zhang A M 2014 Acta Phys. Sin. 63 074703 (in Chinese) [史冬岩, 王志凯, 张阿漫 2014 物理学报 63 074703]
[17] Le G G, Oulaid O, Zhang J F 2015 Phys. Rev. E 91 033306
[18] Fu S C, Leung W W F, So R M C 2013 Commun. Comput. Phys. 14 126
[19] Gao D Y, Chen Z Q, Chen L H, Zhang D L 2017 Int. J. Heat Mass Tran. 105 673
[20] Izham M, Fukui T, Morinishi K 2011 J. Fluid Sci. Tech. 6 812
[21] Nie D M, Lin J Z 2010 Chin. Phys. Lett. 27 104701
[22] Fang H P, Wan R Z, Fan L W 2000 Chin. Phys. 9 515
[23] Szalmas L 2007 Int. J. Mod. Phys. C 18 15
[24] Tao S, Guo Z L 2015 Phys. Rev. E 91 043305
[25] Guo Z L, Shi B C, Zheng C G 2011 Comput. Math. Appl. 61 3519
[26] Suga K 2013 Fluid Dyn. Res. 45 034501
[27] Yang W L, Li H X, Zhang T J, Elfadel I M 2015 ASME 2015 13th International Conference on Nanochannels, Microchannels, and Minichannels San Francisco, CA, USA, July 6-9, 2015 pV001T04A001
[28] Buick J M, Greated C A 2000 Phys. Rev. E 61 5307
[29] Guo Z L, Zheng C G, Shi B C 2002 Phys. Rev. E 65 046308
[30] Sun Y H, Barber R W, Emerson D R 2005 Phys. Fluids 17 047102
[31] Beskok A, Karniadakis G E 1994 J. Thermophys. Heat Tr. 8 647
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