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Towards aeraulic simulations at urban scale using the lattice Boltzmann method

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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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\(C_S\) :

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

\(B\) :


\(t\) :


\(x,y,z\) :

Relative to direction

\(\infty \) :



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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).

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