Citation: Andrea Lo Giudice, Roberto Nuca, Luigi Preziosi, Nicolas Coste. Wind-blown particulate transport: A review of computational fluid dynamics models[J]. Mathematics in Engineering, 2019, 1(3): 508-547. doi: 10.3934/mine.2019.3.508
[1] | Abadie MO, Mendes N (2008) Numerical assessment of turbulence effect on the evaluation of wind-driven rain specific catch ratio. Int Commun Heat Mass Transfer 35: 1253–1261. doi: 10.1016/j.icheatmasstransfer.2008.08.013 |
[2] | Al-Hajraf S, Rubini P (2001) Three-dimensional homogeneous two-phase flow modelling of drifting sand around an open gate. WIT Trans Eng Sci 30: 309–325. |
[3] | Alhajraf S (2000) Numerical simulation of drifting sand, PhD thesis, Cranfield University. |
[4] | Anderson RS, Haff PK (1988) Simulation of eolian saltation. Science 241: 820–823. doi: 10.1126/science.241.4867.820 |
[5] | Anderson RS, Hallet B (1986) Sediment transport by wind: Toward a general model. Geol Soc Am Bull 97: 523–535. doi: 10.1130/0016-7606(1986)97<523:STBWTA>2.0.CO;2 |
[6] | Andreotti B, Claudin P, Douady S (2002a) Selection of dune shapes and velocities part 1: Dynamics of sand, wind and barchans. Eur Phys J B 28: 321–339. |
[7] | Andreotti B, Claudin P, Douady S (2002b) Selection of dune shapes and velocities part 2: A two-dimensional modelling. Eur Phys J B 28: 341–352. |
[8] | Andrews M, O'rourke P (1996) The multiphase particle-in-cell (MP-PIC) method for dense particulate flows. Int J Multiphase Flow 22: 379–402. doi: 10.1016/0301-9322(95)00072-0 |
[9] | Arastoopour H, Pakdel P, Adewumi M (1990) Hydrodynamic analysis of dilute gas-solids flow in a vertical pipe. Powder Technol 62: 163–170. doi: 10.1016/0032-5910(90)80080-I |
[10] | Balachandar S, Eaton J (2010) Turbulent dispersed multiphase flow. Annu Rev Fluid Mech 42: 111–133. doi: 10.1146/annurev.fluid.010908.165243 |
[11] | Bang B, Nielsen A, Sundsbø P, et al. (1994) Computer simulation of wind speed, wind pressure and snow accumulation around buildings (SNOW-SIM). Energy Build 21: 235–243. doi: 10.1016/0378-7788(94)90039-6 |
[12] | Barnea E, Mizrahi J (1973) A generalized approach to the fluid dynamics of particulate systems: Part 1. General correlation for fluidization and sedimentation in solid multiparticle systems. Chem Eng J 5: 171–189. |
[13] | Benyahia S, Syamlal M, O'Brien TJ (2006) Extension of Hill-Koch-Ladd drag correlation over all ranges of Reynolds number and solids volume fraction. Powder Technol 162: 166–174. doi: 10.1016/j.powtec.2005.12.014 |
[14] | Beyers J, Sundsbø P (2004) Numerical simulation of three-dimensional, transient snow drifting around a cube. J Wind Eng Ind Aerod 92: 725–747. doi: 10.1016/j.jweia.2004.03.011 |
[15] | Beyers M, Waechter B (2008) Modeling transient snowdrift development around complex three-dimensional structures. J Wind Eng Ind Aerod 96: 1603–1615. doi: 10.1016/j.jweia.2008.02.032 |
[16] | Blocken B (2014) 50 years of computational wind engineering: past, present and future. J Wind Eng Ind Aerod 129: 69–102. doi: 10.1016/j.jweia.2014.03.008 |
[17] | Blocken B, Carmeliet J (2010) Overview of three state-of-the-art wind-driven rain assessment models and comparison based on model theory. Build Environ 45: 691–703. doi: 10.1016/j.buildenv.2009.08.007 |
[18] | Blocken B, Stathopoulos T, Carmeliet J (2007) CFD simulation of the atmospheric boundary layer: Wall function problems. Atmos Environ 41: 238–252. doi: 10.1016/j.atmosenv.2006.08.019 |
[19] | Boutanios Z, Jasak H (2017) Two-way coupled Eulerian-Eulerian simulations of drifting snow with viscous treatment of the snow phase. J Wind Eng Ind Aerod 169: 67–76. doi: 10.1016/j.jweia.2017.07.006 |
[20] | Businger J, Wyngaard J, Izumi Y, et al. (1971) Flux profile relationships in the atmospheric surface layer. J Atmos Sci 28: 181–189. doi: 10.1175/1520-0469(1971)028<0181:FPRITA>2.0.CO;2 |
[21] | Canuto C, Lo Giudice A (2018) A multi-timestep robin-robin domain decomposition method for time dependent advection-diffusion problems. App Math Comput (In press). |
[22] | Chapman S, Cowling T (1970) The Mathematical Theory of Non-uniform Gases, Cambridge Mathematical Library. |
[23] | Chen C, Wood P (1985) A urbulence closure model for dilute gas particle flows. Can J Chem Eng 63: 349–360. Available from: https://doi.org/10.1002/cjce.5450630301. |
[24] | Choi E (1992) Simulation of wind-driven-rain around a building. J Wind Eng 52: 60–65. |
[25] | Choi E (1997) Numerical modelling of gust effect on wind-driven rain. J Wind Eng Ind Aerod 72: 107–116. doi: 10.1016/S0167-6105(97)00246-8 |
[26] | Creyssels M, Dupont P, Moctar AOE, et al. (2009) Saltating particles in a turbulent boundary layer: Experiment and theory. J Fluid Mech 625: 47–74. doi: 10.1017/S0022112008005491 |
[27] | Deen N, Annaland MVS, der Hoef MV, et al. (2007) Review of discrete particle modeling of fluidized beds. Chem Eng Sci 62: 28–44. doi: 10.1016/j.ces.2006.08.014 |
[28] | Di Felice R (1994) The voidage function for fluid-particle interaction systems. Int J Multiphase Flow 20: 153–159. doi: 10.1016/0301-9322(94)90011-6 |
[29] | Durán O, Parteli EJ, Herrmann HJ (2010) A continuous model for sand dunes: Review, new developments and application to barchan dunes and barchan dune fields. Earth Surf Processes Landforms 35: 1591–1600. doi: 10.1002/esp.2070 |
[30] | Dyer J (1974) A review of flux profile relationships. Boundary-Lay Meteorol 7: 363–372. doi: 10.1007/BF00240838 |
[31] | Elghobashi S (1991) Particle-laden turbulent flows: Direct simulation and closure models, In: Oliemans, R.V.A. Editor, Computational Fluid Dynamics for the Petrochemical Process Industry, Dordrecht: Springer, 91–104. |
[32] | Elghobashi S (1994) On predicting particle-laden turbulent flows. Appl Sci Res 52: 309–329. doi: 10.1007/BF00936835 |
[33] | Ergun S (1952) Fluid flow through packed columns. J Chem Eng Prog 48: 89–94. |
[34] | Faber TE (1995) Fluid Dynamics for Physicists, Cambridge University Press. |
[35] | Farimani AB, Ferreira AD, Sousa AC (2011) Computational modeling of the wind erosion on a sinusoidal pile using a moving boundary method. Geomorphology 130: 299–311. doi: 10.1016/j.geomorph.2011.04.012 |
[36] | Gauer P (1999) Blowing and drifting snow in alpine terrain: a physically-based numerical model and related field measurements. PhD thesis, ETH Zurich, Switzerland. |
[37] | Germano M, Piomelli U, Moin P, et al. (1991) A dynamic subgrid-scale eddy viscosity model. Phys Fluids A 3: 1760–1765. doi: 10.1063/1.857955 |
[38] | Gidaspow D (1994) Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions, Academic press. |
[39] | Gosman A, Lekakou C, Politis S, et al. (1992) Multidimensional modeling of turbulent two-phase flows in stirred vessels. AIChE J 38: 1946–1956. doi: 10.1002/aic.690381210 |
[40] | Hangan H (1999) Wind-driven rain studies. A C-FD-E approach. J Wind Eng Ind Aerod 81: 323–331. doi: 10.1016/S0167-6105(99)00027-6 |
[41] | Ho TD, Dupont P, Ould El Moctar A, et al. (2012) Particle velocity distribution in saltation transport. Phys Rev E 85: 052301. Available from: https://doi.org/10.1103/PhysRevE. 85.052301. |
[42] | Ho TD, Valance A, Dupont P, et al. (2011) Scaling laws in aeolian sand transport. Phys Rev Lett 106: 094501. Available from: https://doi.org/10.1103/PhysRevLett.106.094501. doi: 10.1103/PhysRevLett.106.094501 |
[43] | Ho TD, Valance A, Dupont P, et al. (2014) Aeolian sand transport: Length and height distributions of saltation trajectories. Aeolian Res 12: 65–74. doi: 10.1016/j.aeolia.2013.11.004 |
[44] | Hrenya CM, Sinclair JL (1997) Effects of particle-phase turbulence in gas-solid flows. AlChE J 43: 853–869. Available from: https://aiche.onlinelibrary.wiley.com/doi/abs/10. 1002/aic.690430402. doi: 10.1002/aic.690430402 |
[45] | Hsu TJ, Jenkins JT, Liu PL (2004) On two-phase sediment transport: Sheet flow of massive particles. Proc R Soc A 460: 2223–2250. Available from: https://doi.org/10.1098/rspa. 2003.1273. doi: 10.1098/rspa.2003.1273 |
[46] | Huang S, Li Q (2010a) A new dynamic one-equation subgrid-scale model for large eddy simulations. Int J Numer Methods Eng 81: 835–865. |
[47] | Huang S, Li Q (2010b) Numerical simulations of wind-driven rain on building envelopes based on Eulerian multiphase model. J Wind Eng Ind Aerod 98: 843–857. |
[48] | Huang S, Li Q (2011) Large eddy simulations of wind-driven rain on tall building facades. J Struct Eng 138: 967–983. |
[49] | Iversen J, Greeley R, White BR, et al. (1975) Eolian erosion of the martian surface, part 1: Erosion rate similitude. Icarus 26: 321–331. doi: 10.1016/0019-1035(75)90175-X |
[50] | Iversen J, Rasmussen K (1999) The effect of wind speed and bed slope on sand transport. Sedimentology 46: 723–731. Available from: https://doi.org/10.1046/j.1365-3091. 1999.00245.x. doi: 10.1046/j.1365-3091.1999.00245.x |
[51] | Jenkins JT, Hanes DM (1998) Collisional sheet flows of sediment driven by a turbulent fluid. J Fluid Mech 370: 29–52. Available from: https://doi.org/10.1017/S0022112098001840. doi: 10.1017/S0022112098001840 |
[52] | Ji S, Gerber A, Sousa A (2004) A convection-diffusion CFD model for aeolian particle transport. Int J Numer Methods Fluids 45: 797–817. Available from: https://doi.org/10.1002/fld. 724. doi: 10.1002/fld.724 |
[53] | Jiang H, Dun H, Tong D, et al. (2017) Sand transportation and reverse patterns over leeward face of sand dune. Geomorphology 283: 41–47. doi: 10.1016/j.geomorph.2016.12.030 |
[54] | Jiang H, Huang N, Zhu Y (2014) Analysis of wind-blown sand movement over transverse dunes. Sci Rep 4: 7114. |
[55] | Jones W, Launder B (1972) The prediction of laminarization with a two-equation model of turbulence. Int J Heat Mass Transfer 15: 301–314. doi: 10.1016/0017-9310(72)90076-2 |
[56] | Kang L (2012) Discrete particle model of aeolian sand transport: Comparison of 2D and 2.5D simulations. Geomorphology 139: 536–544. |
[57] | Kang L, Guo L (2006) Eulerian-Lagrangian simulation of aeolian sand transport. Powder Technol 162: 111–120. doi: 10.1016/j.powtec.2005.12.002 |
[58] | Kang L, Liu D (2010) Numerical investigation of particle velocity distributions in aeolian sand transport. Geomorphology 115: 156–171. doi: 10.1016/j.geomorph.2009.10.001 |
[59] | Kang L, Zou X (2011) Vertical distribution of wind-sand interaction forces in aeolian sand transport. Geomorphology 125: 361–373. doi: 10.1016/j.geomorph.2010.09.025 |
[60] | Kato M, Launder B (1993) The modeling of turbulent flow around stationary and vibratingsquare cylinders, In: Ninth Symposium on Turbulent Shear Flows, American Society of Mechanical Engineers, 1–6. |
[61] | Kobayashi H (2005) The subgrid-scale models based on coherent structures for rotating homogeneous turbulence and turbulent channel flow. Phys Fluids 17: 045104. doi: 10.1063/1.1874212 |
[62] | Kobayashi H, Ham F, Wu X (2008) Application of a local sgs model based on coherent structures to complex geometries. Int J Heat Fluid Flow 29: 640–653. doi: 10.1016/j.ijheatfluidflow.2008.02.008 |
[63] | Kok JF, Parteli EJ, Michaels TI, et al. (2012) The physics of wind-blown sand and dust. Rep Prog Phys 75: 106901. doi: 10.1088/0034-4885/75/10/106901 |
[64] | Kolmogorov AN (1941) The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl Akad Nauk SSSR 30: 299–303. |
[65] | Kubilay A, Carmeliet J, Derome D (2017) Computational fluid dynamics simulations of wind-driven rain on a mid-rise residential building with various types of facade details. J Build Perform Simul 10: 125–143. doi: 10.1080/19401493.2016.1152304 |
[66] | Kubilay A, Derome D, Blocken B, et al. (2013) CFD simulation and validation of wind-driven rain on a building facade with an Eulerian multiphase model. Build Environ 61: 69–81. doi: 10.1016/j.buildenv.2012.12.005 |
[67] | Kubilay A, Derome D, Blocken B, et al. (2014) Numerical simulations of wind-driven rain on an array of low-rise cubic buildings and validation by field measurements. Build Environ 81: 283–295. doi: 10.1016/j.buildenv.2014.07.008 |
[68] | Kubilay A, Derome D, Blocken B, et al. (2015a) Numerical modeling of turbulent dispersion for wind-driven rain on building facades. Environ Fluid Mech 15: 109–133. |
[69] | Kubilay A, Derome D, Blocken B, et al. (2015b) Wind-driven rain on two parallel wide buildings: field measurements and CFD simulations. J Wind Eng Ind Aerod 146: 11–28. |
[70] | Lakehal D, Mestayer P, Edson J, et al. (1995) Eulero-Lagrangian simulation of raindrop trajectories and impacts within the urban canopy. Atmos Environ 29: 3501–3517. doi: 10.1016/1352-2310(95)00202-A |
[71] | Li Z, Wang Y, Zhang Y, et al. (2014) A numerical study of particle motion and two-phase interaction in aeolian sand transport using a coupled large eddy simulation-discrete element method. Sedimentology 61: 319–332. Available from: https://doi.org/10.1111/sed. 12057. doi: 10.1111/sed.12057 |
[72] | Liston G, Brown R, Dent J (1993) A two-dimensional computational model of turbulent atmospheric surface flows with drifting snow. Ann Glaciol 18: 281–286. doi: 10.3189/S0260305500011654 |
[73] | Lopes A, Oliveira L, Ferreira AD, et al. (2013) Numerical simulation of sand dune erosion. Environ Fluid Mech 13: 145–168. Available from: https://doi.org/10.1007/s10652-012-9263-2. doi: 10.1007/s10652-012-9263-2 |
[74] | Lugo J, Rojas-Solorzano L, Curtis J (2012) Numerical simulation of aeolian saltation within the sediment transport layer using granular kinetic theory. Rev Fac Ing 27: 80–96. |
[75] | Lun CKK, Savage SB, Jeffrey DJ, et al. (1984) Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flowfield. J Fluid Mech 140: 223–256. Available from: https://doi.org/10.1017/S0022112084000586. doi: 10.1017/S0022112084000586 |
[76] | Marval JP, Rojas-Solórzano LR, Curtis JS (2007) Two-dimensional numerical simulation of saltating particles using granular kinetic theory, In: ASME/JSME 2007 5th Joint Fluids Engineering Conference, 929–939. |
[77] | Menter FR (1994) Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 32: 1598–1605. doi: 10.2514/3.12149 |
[78] | Menter FR, Kuntz M, Langtry R (2003) Ten years of industrial experience with the SST turbulence model. Turbul heat mass transfer 4: 625–632. |
[79] | Mochida A, Lun I (2008) Prediction of wind environment and thermal comfort at pedestrian level in urban area. J Wind Eng Ind Aerod 96: 1498–1527. doi: 10.1016/j.jweia.2008.02.033 |
[80] | Monin A, Obukhov A (1954) Basic laws of turbulent mixing in the surface layer of the atmosphere. Contrib Geophys Inst Acad Sci 151: 163–187. |
[81] | Moore I (1995) Numerical modelling of blowing snow around buildings. PhD thesis, University of Leeds. |
[82] | Naaim M, Florence N, Martinez H (1998) Numerical simulation of drifting snow: Erosion and deposition models. Ann Glaciol 26: 191–196. doi: 10.3189/1998AoG26-1-191-196 |
[83] | Nalpanis P,Hunt J,Barrett C (1993) Saltating particles over flat beds. J Fluid Mech 251: 661–685. doi: 10.1017/S0022112093003568 |
[84] | Okaze T, Niiya H, Nishimura K (2018) Development of a large-eddy simulation coupled with Lagrangian snow transport model. J Wind Eng Ind Aerod 183: 35–43. doi: 10.1016/j.jweia.2018.09.027 |
[85] | Okaze T, Takano Y, Mochida A, et al. (2015) Development of a new κ–? model to reproduce the aerodynamic effects of snow particles on a flow field. J Wind Eng Ind Aerod 144: 118–124. |
[86] | Parteli E, Schwämmle V, Herrmann H, et al. (2006) Profile measurement and simulation of a transverse dune field in the lençóis maranhenses. Geomorphology 81: 29–42. doi: 10.1016/j.geomorph.2006.02.015 |
[87] | Pasini JM, Jenkins JT (2005) Aeolian transport with collisional suspension. Philos Trans R Soc A 363: 1625–1646. Available from: https://doi.org/10.1098/rsta.2005.1598. doi: 10.1098/rsta.2005.1598 |
[88] | Patankar N, Joseph D (2001) Modeling and numerical simulation of particulate flows by the Eulerian-Lagrangian approach. Int J Multiphase Flow 27: 1659–1684. doi: 10.1016/S0301-9322(01)00021-0 |
[89] | Pettersson K, Krajnovic S, Kalagasidis A, et al. (2016) Simulating wind-driven rain on building facades using eulerian multiphase with rain phase turbulence model. Build Environ 106: 1–9. doi: 10.1016/j.buildenv.2016.06.012 |
[90] | Pischiutta M, Formaggia L, Nobile F (2011) Mathematical modelling for the evolution of aeolian dunes formed by a mixture of sands: Entrainment-deposition formulation. Commun Appl Ind Math 2: 0003777. |
[91] | Pomeroy J, Gray D (1990) Saltation of snow. Water Resour Res 26: 1583–1594. doi: 10.1029/WR026i007p01583 |
[92] | Preziosi L, Fransos D, Bruno L (2015) A multiphase first order model for non-equilibrium sand erosion, transport and sedimentation. Appl Math Lett 45: 69–75. doi: 10.1016/j.aml.2015.01.011 |
[93] | Sagaut P (2006) Large eddy simulation for incompressible flows: An introduction. Springer Science & Business Media. |
[94] | Sato T, Uematsu T, Nakata T, et al. (1993) Three dimensional numerical simulation of snowdrift, In: Murakami, S. Editor, Computational Wind Engineering 1, Elsevier, Oxford, 741–746. Available from: https://doi.org/10.1016/B978-0-444-81688-7.50082-6. |
[95] | Sauermann G, Andrade J, Maia L, et al. (2003) Wind velocity and sand transport on a barchan dune. Geomorphology 54: 245–255. doi: 10.1016/S0169-555X(02)00359-8 |
[96] | Sauermann G, Kroy K, Herrmann HJ (2001) Continuum saltation model for sand dunes. Phys Rev E 64: 031305. doi: 10.1103/PhysRevE.64.031305 |
[97] | Schlichting H, Gersten K (2016) Boundary-Layer Theory, Springer. |
[98] | Shi X, Xi P, Wu J (2015) A lattice Boltzmann-Saltation model and its simulation of aeolian saltation at porous fences. Theor Comput Fluid Dyn 29: 1–20. |
[99] | Shih TH, Liou WW, Shabbir A, et al. (1995) A new k-? eddy viscosity model for high Reynolds number turbulent flows. Comput Fluids 24: 227–238. |
[100] | Smagorinsky J (1963) General circulation experiments with the primitive equations: I. the basic experiment. Mon Weather Rev 91: 99–164. doi: 10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2 |
[101] | Sun Q, Wang G, Xu Y (2001) DEM applications to aeolian sediment transport and impact process in saltation. Partl Sci Technol 19: 339–353. doi: 10.1080/02726350290057877 |
[102] | Sun X, He R, Wu Y (2018) Numerical simulation of snowdrift on a membrane roof and the mechanical performance under snow loads. Cold Reg Sci Technol 150: 15–24. doi: 10.1016/j.coldregions.2017.09.007 |
[103] | Sundsbø P (1998) Numerical simulations of wind deflection fins to control snow accumulation in building steps. J Wind Eng Ind Aerod 74: 543–552. |
[104] | Surry D, Inculet D, Skerlj P, et al. (1994) Wind, rain and the building envelope: A status report of ongoing research at the university of western ontario. J Wind Eng Ind Aerod 53: 19–36. doi: 10.1016/0167-6105(94)90016-7 |
[105] | Syamlal M, O' Brien T (1987) The derivation of a drag coefficient formula from velocity-voidage correlations. Tech Note, US Department of Energy, Office of Fossil Energy, NETL, Morgantown, WV. |
[106] | Thiis TK (2000) A comparison of numerical simulations and full-scale measurements of snowdrifts around buildings. Wind Struct 3: 73–81. doi: 10.12989/was.2000.3.2.073 |
[107] | Tominaga Y, Okaze T, Mochida A (2011) CFD modeling of snowdrift around a building: An overview of models and evaluation of a new approach. Build Environ 46: 899–910. doi: 10.1016/j.buildenv.2010.10.020 |
[108] | Tong D, Huang N (2012) Numerical simulation of saltating particles in atmospheric boundary layer over flat bed and sand ripples. J Geophys Res Atmos 117. Available from: https://doi. org/10.1029/2011JD017424. |
[109] | Uematsu T, Nakata T, Takeuchi K, et al. (1991) Three-dimensional numerical simulation of snowdrift. Cold Reg Sci Technol 20: 65–73. doi: 10.1016/0165-232X(91)90057-N |
[110] | Vinkovic I, Aguirre C, Ayrault M, et al. (2006) Large-eddy simulation of the dispersion of solid particles in a turbulent boundary layer. Boundary-layer Meteorol 121: 283–311. doi: 10.1007/s10546-006-9072-6 |
[111] | Wang H, Hou X, Deng Y (2015) Numerical simulations of wind-driven rain on building facades under various oblique winds based on Eulerian multiphase model. J Wind Eng Ind Aerod 142: 82–92. doi: 10.1016/j.jweia.2015.02.006 |
[112] | Wen C, Yu Y (1966) A generalized method for predicting the minimum fluidization velocity. AIChE J 12: 610–612. doi: 10.1002/aic.690120343 |
[113] | Werner B (1990) A Steady-State model of Wind-Blown sand transport. J Geol 98: 1–17. Available from: https://doi.org/10.1086/629371. doi: 10.1086/629371 |
[114] | Wilcox D (2008) Formulation of the k-ω turbulence model revisited. AIAA J 46: 2823–2838. Available from: https://doi.org/10.2514/1.36541. doi: 10.2514/1.36541 |
[115] | Wilcox DC (1988) Reassessment of the scale-determining equation for advanced turbulence models. AIAA J 26: 1299–1310. doi: 10.2514/3.10041 |
[116] | Wilcox DC (1998) Turbulence Modeling for CFD, 2nd Edition, DCW industries La Canada, California. |
[117] | Xiao F, Guo L, Li D, et al. (2012) Discrete particle simulation of mixed sand transport. Particuology 10: 221–228. doi: 10.1016/j.partic.2011.10.004 |
[118] | Yakhot V, Orszag S (1986) Renormalization group analysis of turbulence. i. basic theory. J Sci Comput 1: 3–51. Available from: https://doi.org/10.1007/BF01061452. |
[119] | Zhou X,Kang L,Gu M,et al. (2016a) Numerical simulation and wind tunnel test for redistribution of snow on a flat roof. J Wind Eng Ind Aerod 153: 92–105. |
[120] | Zhou X, Zhang Y, Wang Y, et al. (2016b) 3D numerical simulation of the evolutionary process of aeolian downsized crescent-shaped dunes. Aeolian Res 21: 45–52. |