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Towards aeraulic simulations at urban scale using the lattice Boltzmann method

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Abstract

The lattice Boltzmann method (LBM) is an innovative approach in computational fluid dynamics (CFD). Due to the underlying lattice structure, the LBM is inherently parallel and therefore well suited for high performance computing. Its application to outdoor aeraulic studies is promising, e.g. applied on complex urban configurations, as an alternative approach to the commonplace Reynolds-averaged Navier–Stokes and large eddy simulation methods based on the Navier–Stokes equations. Emerging many-core devices, such as graphic processing units (GPUs), nowadays make possible to run very large scale simulations on rather inexpensive hardware. In this paper, we present simulation results obtained using our multi-GPU LBM solver. For validation purpose, we study the flow around a wall-mounted cube and show agreement with previously published experimental results. Furthermore, we discuss larger scale flow simulations involving nine cubes which demonstrate the practicability of CFD simulations in building external aeraulics.

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Abbreviations

\(C_S\) :

Smagorinsky constant

\(c_s\) :

Speed of sound (\(\hbox {m}\,\hbox {s}^{-1}\))

\(\delta t\) :

Time step (s)

\(\delta x\) :

Mesh size (m)

\(e\) :

Energy (J)

\(\mathbf{F}\) :

External force

\(f\) :

Distribution function

\(H\) :

Height of the cube (m)

\(h\) :

Height of the channel (m)

\(\mathbf{j}\) :

Fluid momentum (\(\hbox {kg}\,\hbox {m}^{-2}\,\hbox {s}^{-1}\))

\(m\) :

Mass of the particle (kg)

\({{\mathsf {P}}}\) :

Strain rate tensor

\(p_{xx}\) :

Related to the strain rate tensor

\(p\) :

Mean pressure (Pa)

\(\mathbf{q}\) :

Heat flux (\(\hbox {W}\,\hbox {m}^{-2}\))

\(\hbox {Re}\) :

Reynolds number (–)

\(r\) :

Averaged pressure relative variation (–)

\(s\) :

Relaxation rate

\(T_0\) :

Turn-over time (s)

\(u_0\) :

Maximum inlet velocity (\(\hbox {m}\,\hbox {s}^{-1}\))

\(\mathbf{u}\) :

Fluid velocity (\(\hbox {m}\,\hbox {s}^{-1}\))

\(x,y,z\) :

Position (m)

\(\varOmega \) :

Collision operator

\(\varvec{\xi }_\alpha \) :

Particle velocity (\(\hbox {m}\,\hbox {s}^{-1}\))

\(\rho \) :

Fluid density (\(\hbox {kg}\,\hbox {m}^{-3}\))

\(\varepsilon \) :

Energy square (\(\hbox {J}^{2}\))

\(\nu \) :

Kinematic viscosity (\(\hbox {m}^{2}\,\hbox {s}^{-1}\))

\(\tau \) :

Relaxation time (s)

\(0\) :

Molecular or inflow

\(\alpha \) :

Associated to the particle velocities \(\varvec{\xi }_\alpha \)

\(B\) :

Bulk

\(t\) :

Turbulent

\(x,y,z\) :

Relative to direction

\(\infty \) :

Free-stream

References

  1. 1.

    Bhatnagar PL, Gross EP, Krook M (1954) A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys Rev 94(3):511–525

  2. 2.

    Blocken B, Persoon J (2009) Pedestrian wind comfort around a large football stadium in an urban environment: CFD simulation, validation and application of the new Dutch wind nuisance standard. J Wind Eng Ind Aerodyn 97(5):255–270

  3. 3.

    Blocken B, Stathopoulos T, Carmeliet J, Hensen J (2011) Application of computational fluid dynamics in building performance simulation for the outdoor environment: an overview. J Build Perform Simul 4(2):157–184

  4. 4.

    Cercignani C (1987) The Boltzmann equation ans its applications. Springer, Berlin

  5. 5.

    Chen S, Doolen GD (1998) Lattice boltzmann method for fluid flows. Ann Rev Fluid Mech 30(1):329–364

  6. 6.

    Crouse B, Krafczyk M, Kühner S, Rank E, Van Treeck C (2002) Indoor air flow analysis based on lattice Boltzmann methods. Energy Build 34(9):941–949

  7. 7.

    d’Humières D (1994) Generalized lattice-Boltzmann equations. Rarefied gas dynamics—theory and simulations pp 450–458

  8. 8.

    d’Humières D, Ginzburg I, Krafczyk M, Lallemand P, Luo L (2002) Multiple-relaxation-time lattice Boltzmann models in three dimensions. Philos Trans 360:437–451

  9. 9.

    Fan Z, Qiu F, Kaufman A, Yoakum-Stover S (2004) GPU cluster for high performance computing. In: Proceedings of the 2004 ACM/IEEE conference on supercomputing, IEEE Computer Society, p 47

  10. 10.

    Frisch U, Hasslacher B, Pomeau Y (1986) Lattice-gas automata for the Navier-Stokes equation. Phys Rev Lett 56(14):1505–1508

  11. 11.

    Gousseau P, Blocken B, Stathopoulos T, van Heijst G (2011) CFD simulation of near-field pollutant dispersion on a high-resolution grid: a case study by LES and RANS for a building group in downtown Montreal. Atmos Environ 45(2):428–438

  12. 12.

    Krafczyk M, Tölke J, Luo L (2003) Large-eddy simulations with a multiple-relaxation-time LBE model. Int J Mod Phys B 17(1):33–40

  13. 13.

    Lallemand P, Luo L (2000) Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys Rev E 61(6):6546

  14. 14.

    Lee V, Kim C, Chhugani J, Deisher M, Kim D, Nguyen A, Satish N, Smelyanskiy M, Chennupaty S, Hammarlund P (2010) Debunking the 100X GPU vs. CPU myth: an evaluation of throughput computing on CPU and GPU. In: ACM SIGARCH computer architecture news, ACM, vol 38, pp 451–460

  15. 15.

    Martinuzzi R, Tropea C (1993) The flow around surface-mounted, prismatic obstacles placed in a fully developed channel flow. ASME J Fluids Eng 115:85–85

  16. 16.

    McNamara GR, Zanetti G (1988) Use of the Boltzmann equation to simulate lattice-gas automata. Phys Rev Lett 61:2332–2335

  17. 17.

    Meinders E, Hanjalic K, Martinuzzi R (1999) Experimental study of the local convection heat transfer from a wall-mounted cube in turbulent channel flow. J Heat Transf 121:564

  18. 18.

    Moonen P, Defraeye T, Dorer V, Blocken B, Carmeliet J (2012) Urban physics: effect of the micro-climate on comfort, health and energy demand. Front Archit Res 1(3):197–228

  19. 19.

    NVIDIA (2010) Compute unified device architecture programming guide version 3.2

  20. 20.

    Obrecht C, Kuznik F, Tourancheau B, Roux JJ (2011a) A new approach to the lattice Boltzmann method for graphics processing units. Comput Math Appl 12(61):3628–3638

  21. 21.

    Obrecht C, Kuznik F, Tourancheau B, Roux JJ (2011b) Global memory access modelling for efficient implementation of the lattice Boltzmann method on graphics processing units. In: Lecture notes in computer science 6449, high performance computing for computational science—VECPAR 2010 revised selected papers, Springer, Berlin, pp 151–161

  22. 22.

    Obrecht C, Kuznik F, Tourancheau B, Roux JJ (2011c) The theLMA project: multi-GPU implementation of the lattice Boltzmann method. Int J High Perform Comput Appl 25(3):295–303

  23. 23.

    Obrecht C, Kuznik F, Tourancheau B, Roux JJ (2011d) Towards urban-scale flow simulations using the lattice Boltzmann method. Proceedings of the BS2011 conference

  24. 24.

    Obrecht C, Kuznik F, Tourancheau B, Roux JJ (2013) Scalable lattice Boltzmann solvers for CUDA GPU clusters. Parallel Comput 39(6–7):259–270

  25. 25.

    Oke T (1987) Boundary layer climates. Routledge, London

  26. 26.

    Onodera N, Aoki T, Shimokawabe T, Kobayashi H (2013) Large-scale LES wind simulation using lattice Boltzmann method for a \(10\,\text{ km }\times 10\, \text{ km }\) area in metropolitan Tokyo. Tech. rep

  27. 27.

    Pan C, Luo L, Miller C (2006) An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Comput Fluids 35(8–9):898–909

  28. 28.

    Pohl T, Deserno F, Thurey N, Rude U, Lammers P, Wellein G, Zeiser T (2004) Performance evaluation of parallel large-scale lattice boltzmann applications on three supercomputing architectures. In: Proceedings of the 2004 ACM/IEEE conference on Supercomputing, IEEE Computer Society, p 21

  29. 29.

    Qian YH, d’Humières D, Lallemand P (1992) Lattice BGK models for Navier–Stokes equation. Europhys Lett 17(6):479–484

  30. 30.

    Sagaut P (2010) Toward advanced subgrid models for Lattice-Boltzmann-based Large-eddy simulation: theoretical formulations. Comput Math Appl 59(7):2194–2199

  31. 31.

    Šarić S, Jakirlić S, Djugum A, Tropea C (2006) Computational analysis of locally forced flow over a wall-mounted hump at high-Re number. Int J Heat Fluid Flow 27(4):707–720

  32. 32.

    Smagorinsky J (1963) General circulation experiments with the primitive equations. Mon Weather Rev 91(3):99–164

  33. 33.

    TheLMA (2010–2013) Thermal LBM on many-core architectures. http://www.thelma-project.info

  34. 34.

    Tölke J, Krafczyk M (2008) TeraFLOP computing on a desktop PC with GPUs for 3D CFD. Int J Comput Fluid Dyn 22(7):443–456

  35. 35.

    Tominaga Y, Stathopoulos T (2010) Numerical simulation of dispersion around an isolated cubic building: model evaluation of RANS and LES. Build Environ 45(10):2231–2239

  36. 36.

    Yakhot A, Liu H, Nikitin N (2006) Turbulent flow around a wall-mounted cube: a direct numerical simulation. Int J Heat Fluid Flow 27(6):994–1009

  37. 37.

    Yoshie R, Mochida A, Tominaga Y, Kataoka H, Harimoto K, Nozu T, Shirasawa T (2007) Cooperative project for CFD prediction of pedestrian wind environment in the Architectural Institute of Japan. J Wind Eng Ind Aerodyn 95(9):1551–1578

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Correspondence to Christian Obrecht.

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Obrecht, C., Kuznik, F., Merlier, L. et al. Towards aeraulic simulations at urban scale using the lattice Boltzmann method. Environ Fluid Mech 15, 753–770 (2015). https://doi.org/10.1007/s10652-014-9381-0

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Keywords

  • Computational fluid dynamics
  • Lattice Boltzmann method
  • Urban flow
  • Large eddy simulation
  • High-performance computing