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Citation:
　Yu Han,Qiang Fu,Shuangyin Chen,et al.Progress in Lattice Boltzmann Modeling of Seepage and Freeze-Thaw Processes in Porous Media[J].Journal of Marine Science and Application,2026,(2):433-443.[doi:10.1007/s11804-026-00802-z]
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Progress in Lattice Boltzmann Modeling of Seepage and Freeze-Thaw Processes in Porous Media

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Title:
Progress in Lattice Boltzmann Modeling of Seepage and Freeze-Thaw Processes in Porous Media
Author(s):
Yu Han1;  Qiang Fu1;  Shuangyin Chen2;  Chengwang Xiong2
Affilations:
Author(s):
Yu Han1;  Qiang Fu1;  Shuangyin Chen2;  Chengwang Xiong2
1. School of Water Conservancy and Civil Engineering, Northeast Agricultural University, Harbin, 150030, China;
2. College of Shipbuilding Engineering, Harbin Engineering University, Harbin, 150001, China
Keywords:
Lattice Boltzmann method|Pore scale|Seepage|Freeze-thaw|Multiscale modeling
分类号:
-
DOI:
10.1007/s11804-026-00802-z
Abstract:
Water infiltration and freeze-thaw processes in soils involve pore-scale flow, phase change, and heat transfer. These processes are difficult to describe using conventional continuum methods. Such methods rely on averaged properties and cannot resolve pore-scale interfaces, connectivity changes, or moving phase boundaries. The lattice Boltzmann method (LBM) provides a mesoscopic approach for this type of problem. It represents pore geometry and multiphase interfaces directly on discrete lattices. This feature makes it suitable for simulating saturated and unsaturated seepage, heat transfer under freezing conditions, and freeze-thaw cycles. This paper reviews recent studies on LBM applications in these areas. Different model frameworks and numerical strategies are compared. The results show that LBM can capture pore-scale mechanisms that are not accessible to continuum models. However, several limitations remain. These include high computational cost, unclear physical meaning of some model parameters, and limited experimental validation.

References:

[1] Ahmadi MM, Mohammadi S, Hayati AN (2011) Analytical derivation of tortuosity and permeability of monosized spheres: A volume averaging approach. Phys. Rev. E 83: 026312. https://doi.org/10.1103/PhysRevE.83.026312
[2] Andrade JE, Mital U (2019) Multiscale and multiphysics modeling of soils. In: Lu, N., Mitchell, J. K. (Eds.), Geotechnical Fundamentals for Addressing New World Challenges. Springer International Publishing, Cham, 141-168. https://doi.org/10.1007/978-3-030-06249-1_5
[3] Blunt MJ, Bijeljic B, Dong H, Gharbi O, Iglauer S, Mostaghimi P, Paluszny A, Pentland C (2013) Pore-scale imaging and modelling. Advances in Water Resources, 35th Year Anniversary Issue 51: 197-216. https://doi.org/10.1016/j.advwatres.2012.03.003
[4] Carman PC (1997) Fluid flow through granular beds. Chem. Eng. Res. Des. 75: S32-S48. https://doi.org/10.1016/S0263-8762(97)80003-2
[5] Chen S, Doolen GD (1998) Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30: 329-364. https://doi.org/10.1146/annurev.fluid.30.1.329
[6] Chen Y, Shen C, Lu P, Huang Y (2015) Role of pore structure on liquid flow behaviors in porous media characterized by fractal geometry. Chem. Eng. Process. Process Intensif. 87: 75-80. https://doi.org/10.1016/j.cep.2014.11.014
[7] Chuvilin EM, Bukhanov BA, Mukhametdinova AZ, Grechishcheva ES, Sokolova NS, Alekseev AG, Istomin VA (2022) Freezing point and unfrozen water contents of permafrost soils: Estimation by the water potential method. Cold Reg. Sci. Technol. 196: 103488. https://doi.org/10.1016/jxoldregions.2022.103488
[8] Engemann S, Reichert H, Dosch H, Bilgram J, Honkim?ki V, Snigirev A (2004) Interfacial melting of ice in contact with SiO2. Phys. Rev. Lett. 92: 205701. https://doi.org/10.1103/PhysRevLett.92.205701
[9] Fu Y, Zhao Y, Zhao Y, Han Q (2023) Semi-supervised segmentation of multi-scale soil pores based on a novel receptive field structure. Computers and Electronics in Agriculture 212: 108071. https://doi.org/10.1016/j.compag.2023.108071
[10] Han Y, Cundall PA (2013) LBM-DEM modeling of fluid-solid interaction in porous media. Int. J. Numer. Anal. Methods Geomech. 37: 1391-1407. https://doi.org/10.1002/nag.2096
[11] Han Y, Wang Q, Liu J, Li X (2022) Seepage characteristics in unsaturated dispersive soil considering soil salinity and density impacts: Experimental and numerical combined study. J. Hydrol. 614: 128538. https://doi.org/10.1016/j.jhydrol.2022.128538
[12] Han Y, Wang Y, Liu C, Hu X, An Y, Li Z, Jiang J, Du L (2024) Study on numerical model of thermal conductivity of non-aqueous phase liquids contaminated soils based on mesoscale. International Journal of Thermal Sciences 197: 108790. https://doi.org/10.1016/j.ijthermalsci.2023.108790
[13] Ji Y, Zhou G, Vandeginste V, Zhou Y (2021) Thermal-hydraulic-mechanical coupling behavior and frost heave mitigation in freezing soil. Bull Eng Geol Environ 80: 2701-2713. https://doi.org/10.1007/s10064-020-02092-3
[14] Jiang Z, Lin Y, Chen X, Li S, Cai P, Que Y (2024) Simulating two-phase seepage in undisturbed soil based on lattice boltzmann method and X-ray computed tomography images. Sensors 24: 4156. https://doi.org/10.3390/s24134156
[15] Jiaung WS, Ho JR, Kuo CP (2001) Lattice Boltzmann method for the heat conduction problem with phase change. Numerical Heat Transfer, Part B: Fundamentals 39: 167-187. https://doi.org/10.1080/10407790150503495
[16] Kang Q, Zhang D, Chen S, He X (2002) Lattice Boltzmann simulation of chemical dissolution in porous media. Phys. Rev. E 65: 036318. https://doi.org/10.1103/PhysRevE.65.036318
[17] Kaviany M (1995) Principles of heat transfer in porous media, mechanical engineering series. Springer, New York. https://doi.org/10.1007/978-1-4612-4254-3
[18] Kl?ffel T, Larsbo M, Jarvis N, Barron J (2024) Freeze-thaw effects on pore space and hydraulic properties of compacted soil and potential consequences with climate change. Soil Tillage Res. 239: 106041. https://doi.org/10.1016/j.still.2024.106041
[19] Koponen A, Kataja M, Timonen J (1997) Permeability and effective porosity of porous media. Phys. Rev. E 56: 3319-3325. https://doi.org/10.1103/PhysRevE.56.3319
[20] Leuther F, Schlüter S (2021) Impact of freeze-thaw cycles on soil structure and soil hydraulic properties. SOIL 7: 179-191. https://doi.org/10.5194/soil-7-179-2021
[21] Li KQ, Yin ZY (2025) State of the art of coupled thermo-hydro-mechanical-chemical modelling for frozen soils. Arch Computat Methods Eng 32: 1039-1096. https://doi.org/10.1007/s11831-024-10164-w
[22] Li X, Chen X, Gao Y, Yang J, Ding W, Zvomuya F, Azad N, Li J, He H (2025) Freezing induced soil water redistribution: A review and global meta-analysis. Journal of Hydrology 651: 132594. https://doi.org/10.1016/j.jhydrol.2024.132594
[23] Li X, Wang Q, Hu Y, Fang C (2024) Water-ice phase transition in frozen soils: A mesoscopic numerical study based on lattice Boltzmann method. Geomechanics and Geoengineering 19: 1006-1020. https://doi.org/10.1080/17486025.2024.2339520
[24] Liu B, Fan H, Han W, Zhu L, Zhao X, Zhang Y, Ma R (2021) Linking soil water retention capacity to pore structure characteristics based on X-ray computed tomography: Chinese mollisol under freeze-thaw effect. Geoderma 401: 115170. https://doi.org/10.1016/j.geoderma.2021.115170
[25] Liu H, Valocchi AJ, Kang Q (2012) Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations. Phys. Rev. E 85: 046309. https://doi.org/10.1103/PhysRevE.85.046309
[26] Liu S, Barati R, Zhang C, Kazemi M (2023) Coupled lattice boltzmann modeling framework for pore-scale fluid flow and reactive transport. ACS Omega 8: 13649-13669. https://doi.org/10.1021/acsomega.2c07643
[27] Lorenz E, Hoekstra AG, Caiazzo A (2009) Lees-edwards boundary conditions for lattice boltzmann suspension simulations. Phys. Rev. E 79: 036706. https://doi.org/10.1103/PhysRevE.79.036706
[28] Louren?o RGC, Friggo JR, Constantino PH, Tavares FW (2024) The lattice boltzmann method for mass transfer of miscible multicomponent mixtures: A review. Physics of Fluids 36: 061302. https://doi.org/10.1063/5.0205161
[29] Lv S, Simmer C, Zeng Y, Wen J, Su Z (2022) The simulation of L-band microwave emission of frozen soil during the thawing period with the community microwave emission model (CMEM). Journal of Remote Sensing 2022: 9754341. https://doi.org/10.34133/2022/9754341
[30] Ma K, Jiang M, Liu Z (2023) Accelerating fully resolved simulation of particle-laden flows on heterogeneous computer architectures. Particuology 81: 25-37. https://doi.org/10.1016/j.partic.2022.12.010
[31] Ma Y, Xiao X, Li W, Desbrun M, Liu X (2024) Hybrid LBM-FVM solver for two-phase flow simulation. Journal of Computational Physics 506: 112920. https://doi.org/10.1016/j.jcp.2024.112920
[32] Martys NS, Chen H (1996) Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method. Phys. Rev. E 53: 743-750. https://doi.org/10.1103/PhysRevE.53.743
[33] Patriarche D, Michelot JL, Ledoux E, Savoye S (2004) Diffusion as the main process for mass transport in very low water content argillites: 1. Chloride as a natural tracer for mass transport— diffusion coefficient and concentration measurements in interstitial water. Water Resources Research 40: W01516. https://doi.org/10.1029/2003WR002600
[34] Qin S, Jiang M, Ma K, Su J, Liu Z (2023) Fully resolved simulations of viscoelastic suspensions by an efficient immersed boundary-lattice Boltzmann method. Particuology 75: 26-49. https://doi.org/10.1016/j.partic.2022.06.004
[35] Reinmann AB, Susser JR, Demaria EMC, Templer PH (2019) Declines in northern forest tree growth following snowpack decline and soil freezing. Global Change Biol. 25: 420-430. https://doi.org/10.1111/gcb.14420
[36] Rentschler T, Bartelheim M, Behrens T, Díaz-Zorita Bonilla M, Teuber S, Scholten T, Schmidt K (2022) Contextual spatial modelling in the horizontal and vertical domains. Sci Rep 12: 9496. https://doi.org/10.1038/s41598-022-13514-5
[37] Saruya T, Kurita K, Rempel AW (2014) Indirect measurement of interfacial melting from macroscopic ice observations. Phys. Rev. E 89: 060401. https://doi.org/10.1103/PhysRevE.89.060401
[38] Shan X (2006) Analysis and reduction of the spurious current in a class of multiphase lattice Boltzmann models. Phys. Rev. E 73: 047701. https://doi.org/10.1103/PhysRevE.73.047701
[39] Shan X (1997) Simulation of Rayleigh-Benard convection using a lattice Boltzmann method. Phys. Rev. E 55: 2780-2788. https://doi.org/10.1103/PhysRevE.55.2780
[40] Shan X, Chen H (1993) Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 47: 1815-1819. https://doi.org/10.1103/PhysRevE.47.1815
[41] Shen C, Tian G, Wei S, Zhang D, Song G (2025) An improved model based on lattice boltzmann method for the simulation of water and salt migration in unsaturated soils. Journal of Hydrology 661: 133801. https://doi.org/10.1016/j.jhydrol.2025.133801
[42] Shi Y, Ma W, Zhang L, Yang C, Shang F, Chen C (2024) Change of pore water near the freezing front during soil freezing: Migration and mechanisms. Pedosphere 34: 770-782. https://doi.org/10.1016/j.pedsph.2023.06.009
[43] Song W, Zhang Y, Li B, Fan X (2016) A lattice Boltzmann model for heat and mass transfer phenomena with phase transformations in unsaturated soil during freezing process. Int. J. Heat Mass Transfer 94: 29-38. https://doi.org/10.1016/j.ijheatmasstransfer.2015.11.008
[44] Sun X, She D, Sanz E, Martín-Sotoca JJ, Tarquis AM, Gao L (2023) Multifractal analysis on CT soil images: Fluctuation analysis versus mass distribution. Chaos, Solitons & Fractals 176: 114080. https://doi.org/10.1016/j.chaos.2023.114080
[45] Tian H, Wei C, Wei H, Zhou J (2014) Freezing and thawing characteristics of frozen soils: Bound water content and hysteresis phenomenon. Cold Reg. Sci. Technol. 103: 74-81. https://doi.org/10.1016/j.coldregions.2014.03.007
[46] Torquato S (2020) Predicting transport characteristics of hyperuniform porous media via rigorous microstructure-property relations. Advances in Water Resources 140: 103565. https://doi.org/10.1016/j.advwatres.2020.103565
[47] Wang JP, Liu TH, Wang SH, Luan JY, Dadda A (2023a) Investigation of porosity variation on water retention behaviour of unsaturated granular media by using pore scale Micro-CT and lattice Boltzmann method. J. Hydrol. 626: 130161. https://doi.org/10.1016/j.jhydrol.2023.130161
[48] Wang M, Zhu Y, Mao W, Ye M, Yang J (2023b) Chemical characteristics and reactive transport of soil salt ions in frozen soil during the freeze and thaw period. Journal of Hydrology 621: 129580. https://doi.org/10.1016/j.jhydrol.2023.129580
[49] Wang Q, Milatz M, Hosseini R, Kumar K (2023c) Multiphase lattice Boltzmann modeling of cyclic water retention behavior in unsaturated sand based on X-ray computed tomography. Can. Geotech. J. 60: 1429-1446. https://doi.org/10.1139/cgj-2022-0489
[50] Watanabe K, Flury M (2008) Capillary bundle model of hydraulic conductivity for frozen soil. Water Resour. Res. 44(12): W12402. https://doi.org/10.1029/2008WR007012
[51] Watanabe K, Mizoguchi M (2002) Amount of unfrozen water in frozen porous media saturated with solution. Cold Reg. Sci. Technol. 34: 103-110. https://doi.org/10.1016/S0165-232X(01)00063-5
[52] Xia H, Lai Y, Mousavi-Nezhad M (2024) Meso-scale investigation on the permeability of frozen soils with the lattice Boltzmann method. Physics of Fluids 36: 093616. https://doi.org/10.1063/5.0222658
[53] Xu C, Zhang Z, Zhang S, Jin D, Yang C, Melnikov A, Zhai J (2024) Self-weighting of the overlying soil horizon catalyzed by freeze-thaw cycles leads to silt particle enrichment in the soil profile. CATENA 237, 107815. https://doi.org/10.1016/j.catena.2024.107815
[54] Yin Z, Zhang Q, Laouafa F (2023) Multiscale multiphysics modeling in geotechnical engineering. J. Zhejiang Univ. Sci. A 24: 1-5. https://doi.org/10.1631/jzus.A22MMMiG
[55] Younes N, Wautier A, Wan R, Millet O, Nicot F, Bouchard R (2023) DEM-LBM coupling for partially saturated granular assemblies. Comput. Geotech. 162: 105677. https://doi.org/10.1016/j.compgeo.2023.105677
[56] Zhang W, Man J, Yu X, Fu L, Zheng X, Chen R, Zhuang Y, Zhang J, Liang X, Zhou H (2025) Exploring the role of soil pore structure in methane emissions from rice paddy fields: A combination of x-ray micro-computed tomography and three-dimensional lattice Boltzmann modeling. Physics of Fluids 37: 056614. https://doi.org/10.1063/5.0269678
[57] Zhang X, Crawford JW, Young IM (2016) A lattice Boltzmann model for simulating water flow at pore scale in unsaturated soils. Journal of Hydrology 538: 152-160. https://doi.org/10.1016/j.jhydrol.2016.04.013
[58] Zheng J, Zhang W, Zhang G, Yu Y, Wang S (2016) Effect of porous structure on rarefied gas flow in porous medium constructed by fractal geometry. J. Nat. Gas Sci. Eng. 34: 1446-1452. https://doi.org/10.1016/j.jngse.2016.07.019
[59] Zhou H, Yu X, Chen C, Lu S, Wu L, Zeng L (2019) Pore-scale lattice Boltzmann modeling of solute transport in saturated biochar amended soil aggregates. Journal of Hydrology 577: 123933. https://doi.org/10.1016/j.jhydrol.2019.123933

Memo

Memo:
Received date:2026-3-28;Accepted date:2026-4-25。<br>Corresponding author:Qiang Fu,E-mail:fuqiang0629@126.com;Chengwang Xiong,E-mail:chengwangxiong@hrbeu.edu.cn
Last Update: 2026-06-08