Numerical Analysis of Gas Flows in a Microchannel Using the Cascaded Lattice Boltzmann Method with Varying Bosanquet Parameter

[1] AGRAWAL, A., DJENIDI, L. & AGRAWAL, A. 2009. Simulation of gas flow in microchannels with a single 90 bend. Computers & Fluids, 38, 1629-1637.

[2] AHMED, I. & BESKOK, A. 2002. Rarefaction, compressibility, and viscous heating in gas microfilters. Journal of Thermophysics and Heat Transfer, 16, 161-170.

[3] ARKILIC, E. B., SCHMIDT, M. A. & BREUER, K. S. 1997. Gaseous slip flow in long microchannels. Journal of Microelectromechanical systems, 6, 167- 178.

[4] ASADOLLAHI, A., RASHIDI, S. & ESFAHANI, J. A. 2017. Condensation process and phasechange in the presence of obstacles inside a minichannel. Meccanica, 52, 2265-2274.

[5] ASADOLLAHI, A., RASHIDI, S. & MOHAMAD, A. A. 2018. Removal of the liquid from a micro-object and controlling the surface wettability by using a rotating shellNumerical simulation by Lattice–Boltzmann method. Journal of Molecular Liquids, 272, 645-655.

[6] BECK, C. & ROEPSTORFF, G. 1990. From stochastic processes to the hydrodynamic equations. Physica A: Statistical Mechanics and its Applications, 165, 270-278.

[7] BESKOK, A. & KARNIADAKIS, G. E. 1999. Report: a model for flows in channels, pipes, and ducts at micro and nano scales. Microscale Thermophysical Engineering, 3, 43-77.

[8] BHATNAGAR, P. L., GROSS, E. P. & KROOK, M. 1954. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Physical review, 94, 511.

[9] CERCIGNANI, C. 1964. Higher order slip according to the linearized Boltzmann equation. CALIFORNIA UNIV BERKELEY INST OF ENGINEERING RESEARCH.

[10] CERCIGNANI, C. 1969. Mathematical methods in kinetic theory, Springer.

[11] CERCIGNANI, C. & DANERI, A. 1963. Flow of a rarefied gas between two parallel plates. Journal of Applied Physics, 34, 3509-3513.

[12] CERCIGNANI, C., LAMPIS, M. & LORENZANI, S. 2004. Variational approach to gas flows in microchannels. Physics of Fluids, 16, 3426- 3437.

[13] DUBOIS, F., FEVRIER, T. & GRAILLE, B. 2015a. Lattice Boltzmann schemes with relative velocities. Communications in Computational Physics, 17, 1088-1112.

[14] DUBOIS, F., FÉVRIER, T. & GRAILLE, B. 2015b. On the stability of a relative velocity lattice Boltzmann scheme for compressible Navier–Stokes equations. Comptes Rendus Mécanique, 343, 599-610.

[15] FEI, L. & LUO, K. H. 2017. Consistent forcing scheme in the cascaded lattice Boltzmann method. Physical Review E, 96, 053307.

[16] GEIER, M., GREINER, A. & KORVINK, J. 2009. A factorized central moment lattice Boltzmann method. The European Physical Journal Special Topics, 171, 55-61.

[17] GEIER, M., GREINER, A. & KORVINK, J. G. 2006. Cascaded digital lattice Boltzmann automata for high Reynolds number flow. Physical Review E, 73, 066705.

[18] GUO, Z., ZHAO, T. & SHI, Y. 2006. Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for microgas flows. Journal of Applied physics, 99, 074903.

[19] GUO, Z. & ZHENG, C. 2008. Analysis of lattice Boltzmann equation for microscale gas flows: relaxation times, boundary conditions and the Knudsen layer. International Journal of Computational Fluid Dynamics, 22, 465- 473.

[20] GUO, Z., ZHENG, C. & SHI, B. 2008. Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow. Physical Review E, 77, 036707.

[21] HADJICONSTANTINOU, N. G. 2003. Comment on Cercignani’s second-order slip coefficient. Physics of Fluids, 15, 2352-2354. [22] HOMAYOON, A., ISFAHANI, A. M., SHIRANI, E. & ASHRAFIZADEH, M. 2011. A novel modified lattice Boltzmann method for simulation of gas flows in wide range of Knudsen number. International Communications in Heat and Mass Transfer, 38, 827-832. [23] HOSSEINI, R., RASHIDI, S. & ESFAHANI, J. A. 2017. A lattice Boltzmann method to simulate combined radiation–force convection heat transfer mode. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39, 3695-3706.

[24] KANDLIKAR, S., GARIMELLA, S., LI, D., COLIN, S. & KING, M. R. 2005. Heat transfer and fluid flow in minichannels and microchannels, elsevier.

[25] LECLAIRE, S., PELLERIN, N., REGGIO, M. & TRÉPANIER, J.-Y. 2014. Multiphase flow modeling of spinodal decomposition based on the cascaded lattice Boltzmann method. Physica A: Statistical Mechanics and its Applications, 406, 307-319.

[26] LEE, T. & LIN, C.-L. 2005. Rarefaction and compressibility effects of the latticeBoltzmann-equation method in a gas microchannel. Physical Review E, 71, 046706. 38 M. Shomali / JHMTR 7 (2020) 25-38

[27] LI, Q., HE, Y., TANG, G. & TAO, W. 2011. Lattice Boltzmann modeling of microchannel flows in the transition flow regime. Microfluidics and nanofluidics, 10, 607-618.

[28] LIU, Q. & HE, Y.-L. 2016. Numerical modelling of microchannel gas flows in the transition flow regime using the cascaded lattice Boltzmann method. arXiv preprint arXiv:1603.01955.

[29] LIU, X. & GUO, Z. 2013. A lattice Boltzmann study of gas flows in a long micro-channel. Computers & Mathematics with Applications, 65, 186-193.

[30] LOCKERBY, D. A., REESE, J. M. & GALLIS, M. A. 2005. The usefulness of higher-order constitutive relations for describing the Knudsen layer. Physics of Fluids, 17, 100609.

[31] LOPEZ, P. 2014. Thermal Lattice Boltzmann Simulation for Rarefied Flow in Microchannels.

[32] LOYALKA, S., PETRELLIS, N. & STORVICK, T. 1975. Some numerical results for the BGK model: Thermal creep and viscous slip problems with arbitrary accomodation at the surface. The Physics of Fluids, 18, 1094- 1099.

[33] LYCETT-BROWN, D. & LUO, K. H. 2014. Multiphase cascaded lattice Boltzmann method. Computers & Mathematics with Applications, 67, 350-362.

[34] LYCETT-BROWN, D., LUO, K. H., LIU, R. & LV, P. 2014. Binary droplet collision simulations by a multiphase cascaded lattice Boltzmann method. Physics of Fluids, 26, 023303.

[35] MAXWELL, J. C. 1879. VII. On stresses in rarified gases arising from inequalities of temperature. Philosophical Transactions of the royal society of London, 231-256.

[36] MICHALIS, V. K., KALARAKIS, A. N., SKOURAS, E. D. & BURGANOS, V. N. 2010. Rarefaction effects on gas viscosity in the Knudsen transition regime. Microfluidics and nanofluidics, 9, 847-853.

[37] MOHAMAD, A. A. 2011. Lattice Boltzmann method: fundamentals and engineering applications with computer codes, Springer Science & Business Media.

[38] NING, Y., PREMNATH, K. N. & PATIL, D. V. 2016. Numerical study of the properties of the central moment lattice Boltzmann method. International Journal for Numerical Methods in Fluids, 82, 59-90.

[39] NIU, X., SHU, C. & CHEW, Y. 2004. A lattice Boltzmann BGK model for simulation of micro flows. EPL (Europhysics Letters), 67, 600.

[40] OHWADA, T., SONE, Y. & AOKI, K. 1989. Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard‐sphere molecules. Physics of Fluids A: Fluid Dynamics, 1, 2042-2049.

[41] PREMNATH, K. N. & BANERJEE, S. 2009. Incorporating forcing terms in cascaded lattice Boltzmann approach by method of central moments. Physical Review E, 80, 036702.

[42] RAHMATI, A. R. & NIAZI, S. 2015. Application and Comparison of Different Lattice Boltzmann Methods on Non-Uniform Meshes for Simulation of Micro Cavity and Micro Channel Flow. Journal of Computational Methods In Engineering, 34, 97-118.

[43] SHEN, C., TIAN, D.-B., XIE, C. & FAN, J. Examination of the LBM in simulation of microchannel flow in transitional regime. ASME 2003 1st International Conference on Microchannels and Minichannels, 2003. American Society of Mechanical Engineers, 405-410.

[44] SHOKOUHMAND, H. & ISFAHANI, A. M. 2011. An improved thermal lattice Boltzmann model for rarefied gas flows in wide range of Knudsen number. International communications in heat and mass transfer, 38, 1463-1469.

[45] STOPS, D. 1970. The mean free path of gas molecules in the transition regime. Journal of Physics D: Applied Physics, 3, 685. [46] TANG, G., ZHANG, Y., GU, X. & EMERSON, D. 2008. Lattice Boltzmann modelling Knudsen layer effect in non-equilibrium flows. EPL (Europhysics Letters), 83, 40008.

[47] ZHANG, Y.-H., GU, X.-J., BARBER, R. W. & EMERSON, D. R. 2006. Capturing Knudsen layer phenomena using a lattice Boltzmann model. Physical Review E, 74, 046704. [48] ZHUO, C. & ZHONG, C. 2013. Filter-matrix lattice Boltzmann model for microchannel gas flows. Physical Review E, 88, 053311.