[1] 
LIU H J, ZOU C, SHI B C, et al. Thermal latticeBGK model based on largeeddy simulation of turbulent natural convection due to internal heat generation[J]. International Journal of Heat and Mass Transfer,2006, 49: 46724680.

[2] 
SHI B C, GUO Z L. Thermal lattice BGK simulation of turbulent natural convection due to internal heat generation [J]. International Journal of Modern Physics B, 2003, 17(1/2): 173177.

[3] 
LADD A J C, VERBERG R. LatticeBoltzmann simulations of particlefluid suspensions [J]. Journal of Statistical Physics, 2001, 104(5/6): 11911251.

[4] 
SHEIKHOLESLAMIM, GORJIBANDPYM, GANJI D D. Lattice Boltzmann method for MHD natural convection heat transfer using nanofluid [J]. Powder Technology,2014, 254: 8293.

[5] 
LIU X L, CHENG P. Lattice Boltzmann simulation for dropwise condensation of vapor along vertical hydrophobic flat plates [J]. International Journal of Heat and Mass Transfer, 2013, 64: 10411052.

[6] 
SEMMA E, EI GANAOUI M, BENNACER R, et al.Investigation of flows in solidification by using the lattice Boltzmann method [J]. International Journal of Thermal Sciences, 2008, 47: 201208.

[7] 
MOUNTRAKIS L, LORENZ E, MALASPINAS O, et al. Parallel performance of an IBLBM suspension simulation framework [J]. Journal of Computational Science,2015, 9: 4550.

[8] 
MENG X H, GUO Z L. Localized lattice Boltzmann equation model for simulating miscible viscous displacement in porous media [J]. International Journal of Heat and Mass Transfer, 2016, 100: 767778.

[9] 
LIU Q, HE Y L. Lattice Boltzmann simulations of convection heat transfer in porous media [J]. Physica A,2017, 465: 742753.

[10] 
CHAI Z H, LIANG H, DU R, et al. A lattice Boltzmann model for twophase flow in porous media [J].SIAM Journal on Scientific Computing, 2019, 41(4):B746B772.

[11] 
GUO Z L, SHU C. Lattice Boltzmann method and its applications in engineering [M]. Singapore: World Scientific Publishing, 2013.

[12] 
SUCCI S. The lattice Boltzmann equation for fluid dynamics and beyond [M]. Oxford: Oxford University Press, 2001.

[13] 
KRGER T, KUSUMAATMAJA H, KUZMIN A, et al.The lattice Boltzmann method: Principles and practice[M]. Switzerland: Springer, 2017.

[14] 
FRISCH U, HASSLACHER B, POMEAU Y. Latticegas automata for the NavierStokes equation [J]. Physical Review Letters, 1986, 56(14): 15051508.

[15] 
BHATNAGAR P L, GROSS E P, KROOKM. A model for collision processes in gases. I. Small amplitude processes in charged and neutral onecomponent systems[J]. Physical Review, 1954, 94(3): 511525.

[16] 
B¨O SCH F, KARLIN I V. Exact lattice Boltzmann equation [J]. Physical Review Letters, 2013, 111:090601.

[17] 
HE X Y, CHEN S Y, DOOLEN G D. A novel thermal model for the lattice Boltzmann method in incompressible limit [J]. Journal of Computational Physics, 1998,146: 282300.

[18] 
HE X Y, LUO L S. Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation [J]. Physical Review E, 1997,56(6): 68116817.

[19] 
YE H F, KUANG B, YANG Y H. Derivation of lattice Boltzmann equation via analytical characteristic integral [J]. Chinese Physics B, 2019, 28(1): 014701.

[20] 
SHAN X W. The mathematical structure of the lattices of the lattice Boltzmann method [J]. Journal of Computational Science, 2016, 17: 475481.

[21] 
HWANG Y H. Macroscopic model and truncation error of discrete Boltzmann method [J]. Journal of Computational Physics, 2016, 322: 5273.

[22] 
YONG W A, ZHAO W F, LUO L S. Theory of the lattice Boltzmann method: Derivation of macroscopic equations via the Maxwell iteration [J]. Physical Review E, 2016, 93: 033310.

[23] 
DELLAR P J. An interpretation and derivation of the lattice Boltzmann method using Strang splitting [J].Computers and Mathematics with Applications, 2013,65: 129141.

[24] 
ARFKEN G, WEBER H, HARRIS F E. Mathematical methods for physicists: A comprehensive guide [M].7th ed. Cambridge, Massachusetts, USA: Academic Press, 2011.
