journal article Open Access Jun 09, 2018

Simulation of stratified flows over a ridge using a lattice Boltzmann model

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Abstract
AbstractA three-dimensional thermal lattice Boltzmann model (TLBM) using multi-relaxation time method was used to simulate stratified atmospheric flows over a ridge. The main objective was to study the efficacy of this method for turbulent flows in the atmospheric boundary layer, complex terrain flows in particular. The simulation results were compared with results obtained using a traditional finite difference method based on the Navier–Stokes equations and with previous laboratory results on stably stratified flows over an isolated ridge. The initial density profile is neutral stratification in the boundary layer, topped with a stable cap and stable stratification aloft. The TLBM simulations produced waves, rotors, and hydraulic jumps in the lee side of the ridge for stably stratified flows, depending on the governing stability parameters. The Smagorinsky turbulence parameterization produced typical turbulence spectra for the velocity components at the lee side of the ridge, and the turbulent flow characteristics of varied stratifications were also analyzed. The comparison of TLBM simulations with other numerical simulations and laboratory studies indicated that TLBM is a viable method for numerical modeling of stratified atmospheric flows. To our knowledge, this is the first TLBM simulation of stratified atmospheric flow over a ridge. The details of the TLBM, its implementation of complex boundaries and the subgrid turbulence parameterizations used in this study are also described in this article.
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References
68
[1]
Chen S, Doolen GD (1998) Lattice Boltzmann method for fluid flows. Annu Rev Fluid Mech 30:329–364 10.1146/annurev.fluid.30.1.329
[2]
Aidun CK, Calusen JR (2010) Lattice Boltzmann method for complex flows. Annu Rev Fluid Mech 42:439–472 10.1146/annurev-fluid-121108-145519
[3]
Luo L.-S, Krafczyk M, Shyy W (2000) Lattice Boltzmann method for computational fluid dynamics. In Blockley R and Shyy W (eds.) Encyclopedia of Aerospace Engineering, Wiley, pp 651–660. ISBN:978-0-470-75440-5
[4]
Guo Z, Shu C (2013) Lattice Boltzmann method and its applications in engineering, Advances in computational fluid dynamics Vol 3. World Scientific Publishing Co. ISBN 978-981-4508-29-2
[5]
Frisch U, Hasslacher B, Pomeau Y (1986) Lattice-gas automata for the Navier-Stokes equations. Phys Rev Lett 56:1505–1508 10.1103/physrevlett.56.1505
[6]
Bhatnagar PL, Gross EP, Krook MA (1954) Model for collision processes in gases. I: small amplitude processes in charged and neutral one-component system. Phys Rev 94:511–525 10.1103/physrev.94.511
[7]
Use of the Boltzmann Equation to Simulate Lattice-Gas Automata

Guy R. McNamara, Gianluigi Zanetti

Physical Review Letters 1988 10.1103/physrevlett.61.2332
[8]
Higuera FJ, Jimenez J (1989) Boltzmann approach to lattice gas simulations. Europhys Lett 9:663–668 10.1209/0295-5075/9/7/009
[9]
Chen H, Chen S, Matthaeus WH (1992) Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Phys Rev A 45:5339–5342 10.1103/physreva.45.r5339
[10]
He X, Luo L-S (1997) Theory of the lattice Boltzmann method: from Boltzmann equation to the lattice Boltzmann equation. Phy Rev E 56:6811–6817 10.1103/physreve.56.6811
[11]
He X, Luo L-S (1997) Lattice Boltzmann for the incompressible Navier-Stokes equation. J Stat Phys 88:927–944 10.1023/b:joss.0000015179.12689.e4
[12]
Guo Z, Shi B, Wang N (2000) Lattice BGK model for incompressible Navier-Stokes equation. J Comput Phys 165:288–306 10.1006/jcph.2000.6616
[13]
He X, Shan X, Doolen GD (1998) Discrete Boltzmann equation model for nonideal gases. Phys Rev E 57:R13(R) 10.1103/physreve.57.r13
[14]
Qian YH, d’Humi`eres D, Lallemand P (1992) Lattice BGK models for Navier-Stokes equation. Europhys Lett 17:479–484 10.1209/0295-5075/17/6/001
[15]
Ziegler DP (1993) Boundary conditions for lattice Boltzmann simulations. J Stat Phys 71:1171–1177 10.1007/bf01049965
[16]
Zou Q, He X (1997) On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys Fluids 9:1591–1598 10.1063/1.869307
[17]
Guo Z, Zheng C, Shi B (2002) An extrapolation method for boundary conditions in lattice Boltzmann method. Phys Fluids 14:2007–2010 10.1063/1.1471914
[18]
Jahanshaloo L, Sidik NAC, Fazeli A, Mahmoud PHA (2016) An overview of boundary implementations in heat and mass transfer. Int Commun Heat Mass Transfer 78:1–12 10.1016/j.icheatmasstransfer.2016.08.014
[19]
Martinez DO, Matthaeus WH, Chen S, Montgomery DC (1994) Comparison of spectral method and lattice Boltzmann simulations of two-dimensional hydrodynamics. Phys Fluids 6:1285–1298 10.1063/1.868296
[20]
Succi S, Amati G, Higuera F (1995) Challenges in lattice Boltzmann computing. J Stat Phys 81:5–16 10.1007/bf02179964
[21]
Hou S, Sterling J, Chen S, Doolen GD (1996) A lattice Boltzmann subgrid model for high Reynolds number flows. Fields Inst Commun 6:151–166
[22]
Basha M, Sidik NAC (2018) Numerical predictions of laminar and turbulent forced convection: lattice Boltzmann simulations using parallel libraries. Int Commun Heat Mass Transfer 116:715–724 10.1016/j.ijheatmasstransfer.2017.09.072
[23]
Shan X, Chen H (1993) Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E 47:1815–1819 10.1103/physreve.47.1815
[24]
Qian YH (1993) Simulating thermo-hydrodynamics with lattice BGK models. J Sci Comp 8:231–241 10.1007/bf01060932
[25]
Yan YY, Zu YQ (2008) Numerical simulation of heat transfer and fluid flow past a rotating isothermal cylinder—a LBM approach. Int J Heat Mass Transfer 51:2519–2536 10.1016/j.ijheatmasstransfer.2007.07.053
[26]
Shan X (1996) Simulation of Rayleigh-Benard convection using a lattice Boltzmann method. Phys Rev E 55:2780–2788 10.1103/physreve.55.2780
[27]
Obrecht C, Kuznik F, Tourancheau B, Roux J-J (2013) Multi-GPU implementation of the lattice Boltzmann method. Comput Math Appl 65:252–261 10.1016/j.camwa.2011.02.020
[28]
King M-F, Khan A, Delbosc N, Gough HL, Halio C, Barlow JF, Noakes CJ (2017) Modeling urban airflow and natural ventilation using a GPU-based lattice Boltzmann method. Build Environ 125 273–284. LBM code running on one GPU was several orders of magnitude faster than Fluent with similar accuracy 10.1016/j.buildenv.2017.08.048
[29]
Inagaki A, Castillo MCL, Yamashita Y, Kanda M, Takimoto H (2012) Large-eddy simulation of coherent flow structures with a cubical canopy. Bound-Layer Meteorol 142(2):207–222 10.1007/s10546-011-9671-8
[30]
Lallemand P, Luo L-S (2000) Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance and stability. Phys Rev E 61:6546–6562 10.1103/physreve.61.6546
[31]
d’Humières D (1992) Generalized lattice Boltzmann equations. In: Shizgal B D, Weave D P (eds.) Rarefied Gas Dynamics: Theory and Simulations, in: Prog. Astronaut. Aeronaut., vol. 159, AIAA, Washington DC, pp 450–458
[32]
d’Humières D, Ginzburg I, Krafczyk M, Lallemand P, Luo L-S (2002) Multiple-relaxation-time lattice Boltzmann models in three dimension. Phil Trans R Soc Lond A 360:437–451 10.1098/rsta.2001.0955
[33]
Luo L-S, Liao W, Chen X, Peng Y, Zhang W (2011) Numerics of the lattice Boltzmann method: effects of collision model on the lattice Boltzmann simulation. Phys Rev E 83:056710 10.1103/physreve.83.056710
[34]
Ginzburg I, Verhaeghe F, d’Humières D (2008) Two-relaxation-time lattice Boltzmann shceme: about parameterization, velocity, pressure and mixed boundary conditions. Commun Comput Phys 3:427–478
[35]
Krafczyk M, Tölke J, Luo L-S (2003) Large-eddy simulations with a multiple-relaxation-time LBE model. Int J Mod Phys B 17:33–39 10.1142/s0217979203017059
[36]
Peng Y, Liao W, Luo L-S, Wang L-P (2010) Comparison of the lattice Boltzmann and pseudo-spectral methods for decaying turbulence: low order statistics. Comput Fluids 39:568–591 10.1016/j.compfluid.2009.10.002
[37]
Ginzburg I (2012) Truncation errors, exact and heuristic stability analysis of two-relaxation-time advecti-diffusion lattice Boltzmann schemes. Comput Phys 11:1439–1502 10.4208/cicp.211210.280611a
[38]
Mezrhab A, Moussaoui MA, Jami M, Naji H, Bouzidi (2010) Double MRT thermal lattice Boltmann method for simulating convective flows. Phys Lett A 374:3499–3507 10.1016/j.physleta.2010.06.059
[39]
Wang J, Wang D, Lallemand P, Luo L-S (2013) Lattice Boltzmann simulations of thermal convective flows in two dimensions. Comput Math Appl 65:262–286 10.1016/j.camwa.2012.07.001
[40]
Contrino D, Lallemand P, Asinari P, Luo S-L (2014) Lattice Boltzmann simulations of the thermally driven 2D square cavity at high Rayleigh numbers. J Comput Phys 275:257–272 10.1016/j.jcp.2014.06.047
[41]
Queney P (1948) The problem of air flow over mountains: a summary of theoretical studies. Bull Am Meteorol Soc 29:16–26 10.1175/1520-0477-29.1.16
[42]
Sorer RS (1949) Theory of lee-waves of mountains. Q J R Meteorol Soc 75:41–56 10.1002/qj.49707532308
[43]
Long RR (1953) Some aspects of the flow of stratified fluids I, A theoretical investigation. Tellus 5:42–58 10.3402/tellusa.v5i1.8563
[44]
Smith RB (1976) The generation of lee waves by the Blue Ridge. J Atmos Sci 33:507–519 10.1175/1520-0469(1976)033<0507:tgolwb>2.0.co;2
[45]
Klemp JB, Lilly DK (1975) The dynamics of wave induced downslope winds. J Atmos Sci 32:320–339 10.1175/1520-0469(1975)032<0320:tdowid>2.0.co;2
[46]
Durran DR (1986) Another look at downslope windstorms. Part I: the development of analogs to supercritical flow in an infinitely deep, continuously stratified fluid. J Atmos Sci 43:2527–2543 10.1175/1520-0469(1986)043<2527:aladwp>2.0.co;2
[47]
Doyle JD, Durran DR (2002) The dynamics of mountain-wave-induced rotors. J Atmos Sci 59:186–201 10.1175/1520-0469(2002)059<0186:tdomwi>2.0.co;2
[48]
Vosper SB (2004) Inversion effects on mountain lee waves. Q J R Meteorol Soc 130:1723–1748 10.1256/qj.03.63
[49]
Grubišič V, Stiperski I (2009) Lee-wave resonances over double bell-shaped obstacles. J Atmos Sci 66:1205–1228 10.1175/2008jas2885.1
[50]
Durran DR (2003) Lee waves and mountain waves. In: Holton JR, Pyle J, Curry (eds.) Encyclopedia Atmos Sci, Elsevier Science. pp 1161–1169 10.1016/b0-12-227090-8/00202-5

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Published
Jun 09, 2018
Vol/Issue
20(5)
Pages
1333-1355
License
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Funding
Office of Naval Research Award: N00014-11-1-0709
Cite This Article
Yansen Wang, Benjamin T. MacCall, Christopher M. Hocut, et al. (2018). Simulation of stratified flows over a ridge using a lattice Boltzmann model. Environmental Fluid Mechanics, 20(5), 1333-1355. https://doi.org/10.1007/s10652-018-9599-3
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