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Streamlining meshing methodologies for annual urban CFD simulations
Patrick Kastner, Timur Dogan
Cornell University, Ithaca, NY, USA
Abstract:
For environmental CFD simulations, it is considered best practice to use a box-shaped wind tunnel as simulation
domain. A box-shaped wind tunnel, however, shows drawbacks when it comes to simulating air flow from several wind directions
— remeshing and additional preprocessing steps may be necessary and can be considerable time constraints. We utilize a
routine implemented in Grasshopper to create a cylindrical computational mesh that allows for the simulation of arbitrary
wind directions in a streamlined manner with the open source software OpenFOAM. We estimate the time savings that are
possible along with specific mesh properties to take advantage of the proposed method. For validation purposes, commonly
used wind tunnel data are presented. A proof of concept tool is implemented in the Rhinoceros CAD modeling environment and
will be released publicly.
Keywords: CFD, meshing, urban, cylindrical, box-shaped, annual, wind tunnel
INT RODUCTION
Urbanization and population growth, along with a massive
predicted construction volume can be seen as a unique op-
portunity to improve the built environment and quality of
life through integrated, and well-informed architectural ur-
ban design processes. Such processes lead to high quality,
climate-adaptive architecture that uses passive means to pro-
vide comfortable environments which in turn are character-
ized by smaller carbon footprints. In areas where the largest
construction volumes are expected, notably in subtropical
and tropical climates, natural ventilation (NV) is one of the
most efficient ways of cooling and promises a significant
energy saving potential. In such areas, studies have shown
the possibility of saving up to 50 % energy compared to me-
chanical ventilation (Cardinale et al.,2003;Oropeza-Perez
and Østergaard,2014).
Architectural design for good NV supply remains challeng-
ing due to its many physical and computational variables
involved and the expert knowledge needed. As a result, the
simulations are expensive, and they are usually not employed
until the very end of the design process — often resulting in
design alterations no longer being feasible. Thus, to incorpo-
rate natural ventilation analysis into early design stages, the
workflows for annual wind analysis need to be (1) stream-
lined; and (2) the time to produce actionable results needs
to be reduced. In this study, we propose a novel methodol-
ogy to reduce the overall preprocessing and simulation time
of annual urban wind simulations by utilizing the Compu-
tational Fluid Dynamics (CFD) software OpenFOAM and
optimizing the shape and the creation of the simulation do-
main. Moreover, we investigate meshing issues that might
occur while employing cylindrical meshes for urban CFD
simulations. In doing this, we hope to create a robust work-
flow that expedites annual wind flow analysis into existing
urban energy simulations as shown in figure 1.
METHODOLOGY
Building energy modeling (BEM) packages like Energy Plus
and TRNSYS come with capable airflow network (AFN)
solutions for natural ventilation evaluation in multi-zone
building energy models. These solutions rely on pressure
coefficient arrays for different wind directions and exterior
simulation nodes. For simple box-shaped buildings without
contextual obstructions, lookup tables and fast methods for
surface-averaged pressure coefficient generation exist. For
instance, two examples are EnergyPlus (Swami and Chan-
dra,1988) or the wind-pressure distribution model CpGen++
developed for COMIS (Grosso,1992). Since then, many
attempts have been made to deal with air flow sheltering ef-
fects for simplified urban geometries and there is an evolving
literature about wind pressure coefficients for sheltered build-
ings that is summarized extensively by (Costola et al.,2009).
For specific sites, however, further attention is needed to
avoid geometric oversimplification (Cheung and Liu,2011).
In such cases, computationally expensive Fluid Dynamics
(CFD) analysis is required. The expertise to perform such
an analysis and the associated simulation overhead, often
hinder a wider use of AFN based natural ventilations studies
in urban and building scale design workflows.
CFD is a numerical methodology to calculate desired flow
variables on a number of grid points within a simulation do-
main by solving discretized Navier-Stokes equations (NSE).
The usual steps of a recurrent CFD analysis for an optimiza-
tion process for the built environment consist of:
1. Modeling the building geometry with CAD software
2. Meshing the building geometry and topography
3.
Simulating the problem with appropriately assigned
boundary conditions
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Annual
wind CFD
methodology
Urban CAD model
Annual
wind data
Building
Performance
Simulation software
Scope of this work
Airflow networks
analysis
cpvalues for every
5° wind direction
Estimation of annual
air change rates
Outdoor comfort
analysis
Air velocities with a high
spatial resolution
Figure 1: Schematic of how the scope of this study integrates
with existing workflows.
4.
Post-processing the variables of interest, likely followed
by design alterations and referring back to 1., based on
the results obtained
The geometric optimization of the built environment through
CFD warrants particular attention, especially when it comes
to efficient meshing methodologies. Although several best
practice guidelines for environmental flow problems have
been published over the years (Franke et al.,2004;Franke,
2006;Franke and Baklanov,2007;Franke et al.,2010;Tom-
inaga et al.,2008;Blocken,2015;Ramponi and Blocken,
2012), all of which propose best practices with respect to
domain dimensions, convergence criteria and relaxation fac-
tors. Little focus, however, has been put on how to best
approach annual wind simulations, let alone utilizing results
from CFD studies for more complex analysis like outdoor
comfort studies.
For basic urban CFD simulations, it is considered best prac-
tice to construct a box-shaped virtual wind tunnel with pre-
defined dimensions with respect to the building geometry
that shall be simulated. A widely used best practice pro-
posed by (Tominaga et al.,2008) suggests the size of the
simulation domain to be
z= 6Hmax
,
l= 20Hmax
and
w
given by a blocking ratio of
≤3%
, where z, l, and w are
the dimensions of the domain and
Hmax
is the height of the
tallest building in the building agglomeration to be simu-
lated. The blocking ratio is defined as the ratio of the area
of the building perpendicular to the inlet to the total area
Figure 2: Wind rose of annual wind data from Ranchi, East
India.
of the inlet. A visual representation of those suggestions is
illustrated in figure 4(a).
The result, a box-shaped wind tunnel, however, shows draw-
backs when it comes to simulating air flow from several
wind directions, which may vary from 0
◦
to 359
◦
over the
course of one year depending on the local wind directions.
A seasonal climate without a clear prevalent wind direction
for which simulations from many directions are necessary is
illustrated in figure 2.
As a result, remeshing and/or additional preprocessing steps
with regard to the geometry may be necessary and can be a
considerable overhead, especially for larger urban scale mod-
els and software without a graphical user interface (Open-
FOAM). While (re)meshing of single, exposed building
geometries for few wind directions is manageable, more
complex problems (annual wind analysis with surrounding
urban context) become increasingly complicated to handle.
For such annual analysis, one would usually simulate the
building geometry for a number of wind directions that are
considered to be viable, followed by postprocessing steps
to account for the gaps. There are two viable approaches to
account for different wind directions: one can either alter
the orientation of the building geometry that is placed in the
so-called artificial wind tunnel figure 3(a) or set up an en-
tirely new simulation domain as well as boundary conditions
for each wind direction figure 3(b).
Evidently, both options come with disadvantages. For the
first option, the geometry needs to be remeshed for every
additional wind direction since x and y coordinates of build-
ing elements change respectively. For the second option,
the boundary conditions need to be adjusted to account for
the alteration in wind directions, thus possibly violating the
dimensional rules put forth by (Tominaga et al.,2008). To
circumvent remeshing the geometry for every wind direction,
and thus to reduce overhead, we propose a cylindrical com-
putational mesh that allows for simulating arbitrary wind
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(a) (b)
Figure 3: Top-view of two approaches to account for differ-
ent wind directions. The black square represents the building
geometry.
directions in a streamlined manner, see figure 4(b).
Furthermore, the proposed method automates setup of new
boundary conditions so that a significant amount of time
will be saved to change the boundary conditions in case of
an annual wind analysis (up to 72 or more wind directions).
More specifically, every lateral cylinder patch represents
a 5
◦
change and can be assigned to either inlet or outlet
conditions depending on the wind direction, see figure 9.
Given that, the mesh is reusable for any wind direction that
might be of interest later in time.
By employing a cylindrical mesh while making sure not
to violate the aforementioned best practice dimensions, the
ground area of the mesh is larger and thus characterized
by a higher cell count than one would anticipate with the
conventional approach shown in figure 4(a). The goal of
this study is to quantify the time differences by reducing
overhead with respect to the corresponding mesh proper-
ties. To estimate advantages and drawbacks, we conduct a
Richardson Extrapolation for four stages of mesh refinement
and investigate both a commonly used wind tunnel reference
case by Jiang et al. (2003) for one of those refinements.
REF ER EN CE C AS ES &S IM UL ATION SETUP
CFD simulations are highly sensitive about their BC and the
fineness of the mesh used. Therefore, we validated one of
the three simulation cases against measured data to be able
to examine the accuracy of the results.
All numerical simulations are based on the open source CFD
library OpenFOAM, using its steady-state RANS models
and solvers in combination with a
k−w−SST
turbulence
model. While we are aware of the limited applicability of
the RANS equations for environmental flows, it is impor-
tant to emphasize that this study focuses on early design
methods for the built environment, thus emphasizing the
interest in simulation time rather than strict accuracy. The
pressure-velocity coupling was calculated with the SIMPLE
algorithm using three non-orthogonal correctors. Buoyancy
effects were neglected due to air velocities that are well
above
1.8 m s−1
(Tecle et al.,2013;Boulard et al.,1996).
Furthermore, we assumed that convergence was obtained
when reaching residuals of
1×10−4 f
or
p
and
1×10−5 f
or
the remaining parameters. The relaxation factors were cho-
sen to be 0.7 for pand 0.3 for U,kand ω.
All simulations were done on an AMD Ryzen Threadripper
1950X 16-Core Processor running Windows 10. We used
the Docker Version 17.12.0-ce-win47 (15139) to run Open-
FOAM 4.1. At most, we ran a maximum of four OpenFOAM
instances at a time on single CPUs on separate threads to
avoid simulation times being affected by other processes
hogging resources.
Jiang et al. (2003) conducted an extensive study in an atmo-
spheric boundary layer (ABL) wind tunnel (WT) in which
a scale model had been investigated experimentally. One
scale model that had been used is a cuboid with two open-
ings for investigations of the ”cross-ventilation” behavior,
see figure 5. The geometry in figure 5was modeled in
Rhinoceros 5
with infinitesimally thin walls, neglecting the
wall dimensions of the wind tunnel scale model of
6 mm
.
The plugin Grasshopper was used to automate the pre-
processing, including the assignment of boundary condi-
tions. The mesh was created by using the blockMesh utility
for the background mesh and snappyHexMesh to subse-
quently snap the background mesh to the building geometry.
The dimensions of the box-shaped simulation domain are
5.75 ×1.16 ×1.5 m
. The domain inlet was set to an ABL
profile for
U
,
k
, and
ω
. At the outlet of the computational
domain, a constant pressure is assumed, while the other vari-
ables are assumed to be zero-gradient. The ground and the
building walls use the same boundary conditions, a no-slip
condition for velocity, a zero-gradient condition for the pres-
sure and wall functions for
k
and
ω
. For the
νt
, an intelligent
wall function was used. The front, back, and top faces are
set to symmetry boundary conditions for all variables. The
kinematic viscosity,
ν
, was set to
1.5 ×10−5
. The turbu-
lence inlet parameters were calculated using the following
equations:
k=(U∗)2
√Cmu
(1)
ε=(U∗)3
κ(z−zmin +z0)(2)
ω=ε
Cmu ·k(3)
where
U∗
is the friction velocity, and
Cmu
is a constant
for the turbulence model being
0.09
. The values used are
summarized in table 1.
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3 % blocking ratio 3 % blocking ratio15 Hmax /
15 Hmax
inlet
outlet
6 Hmax
Hmax
6 Hmax
5 Hmax
(a) (b)
Figure 4: Top-view of the (a) proposed dimensions of simulation domain by (Tominaga et al.,2008) for an arbitrary urban area;
(b) proposed cylindrical simulation domain accounting for the same requirements. The perimeter of the cylindrical domain
consists of 5 straight line segments. A more detailed illustration of the resulting mesh is given in figure 9.
(a) (b)
h = 0.25 m
h/2
h0
Figure 5: (a) Schematic of the reference model that was investigated in the wind tunnel by (Jiang et al.,2003). The dimensions
are given in meters. (b) Vertical section through validation domain for mesh sensitivity purposes.
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Table 1: Turbulence boundary conditions used for the vali-
dation study.
Parameter Value
k0.034 56
0.0835
ω10.42
The approach to model the ABL in OpenFOAM is based on
the following equations (Wallace and Hobbs,2006):
U=U∗
κln z−zmin +z0
z0(4)
U∗=κUref
ln Zref +z0
z0(5)
where
U∗
is the friction velocity,
κ
is the von Karman con-
stant being
= 0.41
,
Uref
is reference velocity at reference
height,
zref
is the reference height and
z0
is the aerodynamic
roughness length.
The atmospheric boundary layer profile of the inlet velocity
in the WT was created by placing Lego Duplo blocks on
the windward side of the scale model. Unfortunately, no
visual documentation is provided to estimate the size or the
resulting z0. Thus, a value of z0= 0.005 was used.
To compare the OpenFOAM results in a quantitative manner,
the data was digitalized as well as interpolated using 50 sam-
pling points. The axis are normalized by height =
0.25 m
and
uref
=
12 m s−1
. For later comparison, the vertical, stream-
wise measurements by Jiang et al. (2003) were taken at
h
2
, as
the most significant deviation from the measured data was
found there, see figure 5. The results were then sampled with
the sample utility using the cellPoint interpolation scheme in
OpenFOAM. Finally, the sampled results were compared to
the experimental values by plotting them against each other
as well as by calculating the coefficient of determination
(R2):
R2= 1 −PN
i=1(yi−ˆyi)2
PN
i=1(yi−¯yi)2,with 0≤R2≤1(6)
The refined meshes were created by varying the size of the
background mesh by factors of two in each direction of the
coordinate system, while keeping the levels of surface and
feature refinements constant. The mesh size for each refine-
ment stage is summarized in table 2, the meshes themselves
are illustrated in figure 6.
The results of the mesh refinement study are depicted in
figure 8in which the normalized domain height is plotted
over the normalized reference velocity. By comparing the
R2
of each refinement stage, it is evident that the accuracy
of the solution increases for finer grids. The finest grid,
however, underpredicts the normalized velocity, especially
in the opening section. In the interest of time and given its
reasonable accuracy, we decided to use the ”coarse” grid
refinement for the subsequent time comparisons.
To provide a standard and consistent approach to report re-
sults of grid convergence studies as well as error estimations,
Roache (1994) suggests to calculate the grid convergence
index (GCI) for the selected grid. The GCI measures the
percentage that the computed value is deviating from the
asymptotic numerical value which is to be interpreted as
an error band. In other words, it measures how much the
solution would change with a further refinement of the grid.
A small GCI indicates that the values are within the asymp-
totic range. The results of the spatial convergence study are
depicted in table 2.
Thus, we may state that the volumetric flow rate for an
ideal mesh would be
0.046 m3h−1
with a numerical error
band of
∼7 %
with respect to the second finest grid. In
the experiment done by Jiang et al. (2003), a volumetric
flow rate of
0.045 m3s−1
was measured which confirms the
results obtained in this study.
Mesh refinements studies for cases with large meshes are
not a trivial task, as the simulation time grows exponentially
with the number of cells. Thus, this method is useful to
estimate the numerical error without conducting a full re-
finement study especially for large-scale simulations. To put
this effort into perspective, we would like to emphasize that
this paper focuses on the comparison of two meshing ap-
proaches, not the accuracy of the results themselves. Hence,
the Richardson Extrapolation shows that the refinements
strategy follows commonly accepted guidelines and that it is
sufficient for our purpose to continue with the coarse mesh.
Detailed information on the grid refinement study may be
found in Kastner (2016).
Figure 9summarizes the dimensions of the box-shaped and
the cylindrical mesh for both case studies. To ensure fair con-
ditions between both approaches, we created the blockMesh
with equal cell sizes in the areas where the buildings were
placed and used identical mesh refinement levels. A visual
representation of both domains after the background mesh
was created is given in figure 9.
RES ULTS
For each simulation case presented, we ran only one wind
direction until the convergence criteria was reached. Table 3
provides a summary of the time comparison between the box-
shaped and the cylindrical wind tunnel of the investigated
mesh refinement. Figure 11 depicts the achieved residuals
of both cases. Figure 10 shows the vertical plot of
uy
for
both cases. The slightly higher
R2
in Figure 10 vs. figure 8
was achieved by employing three mesh layers for the ground
and the building surfaces.
The implementation of the cylindrical simulation domain
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(a) very coarse (b) coarse (c) normal (d) fine
Figure 6: Excerpt of the mesh sizes used in the mesh refinement study.
Table 2: Parameters of grid convergence study. The study was conducted for 4 different mesh sizes: very coarse, coarse, normal
and fine.
r
is the grid refinement ratio and
h
is the normalized grid spacing. Moreover, the Richardson Extrapolation (RE)
predicts the flow rate for an ideal mesh (continuum), estimating the magnitude of the numerical error.
˙v
shows the flow rate
through the windward opening obtained. exp.
=
experiment by (Jiang et al.,2003). cont.
=
continuum. The grid convergence
index refers to the grid number indicated and the subsequent finer grid respectively. The coarse mesh shows reasonable
accuracy and is therefore chosen for further studies.
# type case cell # h r ˙v[m3s−1 ] error (exp.) error (cont.) GCI [%]
1 sim. very coarse 124 456 8 1.3 0.0540 17 % 15 % 11.04
2 sim. coarse 263 919 4 1.6 0.0505 11 % 10 % 6.82
3 sim. normal 1 165 733 2 1.6 0.0485 7 % 6 % 4.94
4 sim. fine 4 940 280 1 - 0.0471 4 % 3 %
- calc. RE - 0 - 0.0456
- meas. experiment - - - 0.0450
Figure 7: Richardson extrapolation of the volumetric flow
rate based on a grid refinement study. The symbol
◦
refers
to the grid sizes in table 2. The symbol
depicts the less
accurate values than the previous refinement stages and
therefore was not used to determine the continuum. The
symbol
◦
is the extrapolated value for the volumetric flow
rate with the discretization error eliminated. The symbol
•
shows the value obtained in the experiment by (Jiang et al.,
2003).
Figure 8: Results of the grid refinement study. Vertical
sample of
uy
at h
/2
for different mesh sizes. Depicted as
•
is the sample from measurements in the wind tunnel.
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box-shaped WT cylindrical WT
x[m]y[m]z[m]radius [m]z[m]
2.75 5.75 1.5 4.125 1.5
Figure 9: The table compares the dimensions of both mesh-
ing approaches considering best practice guidelines. The
illustration shows the corresponding simulation domains
after creating the background mesh with blockMesh.
resulted in a 21 % higher cell count compared to the box-
shaped domain. As expected, the cylindrical domain was
characterized by a higher meshing time; cell count and mesh-
ing time, however, do not scale linearly (21 % vs. 5 %). Fur-
ther, the cylindrical simulation domain is characterized by
a lower simulation time than the box-shaped simulation do-
main. This can most likely be attributed to the differences in
convergence behavior which was worse for the box-shaped
domain, see figure 11. By evaluating the first 200 iterations,
the simulation time per iteration is 16 s for the box-shaped
case and 21 s for the cylindrical case.
It is evident that the box-shaped simulation domain achieves
slightly better accuracy (R2= 96.7%) than the cylindrical
simulation domain (
R2= 94.1
%). Both domains under- or
overestimate regions with high pressure gradients which is
known as a deficiency of the steady-state RANS model.
As a result, for this particular simulation setup, the cylin-
drical domain would be of advantage over the box-shaped
domain from a simulation time perspective.
Table 3: Summary of meshing and simulation times on a
single CPU until convergence criteria was reached. M =
meshing, S = simulation. The units for time are given in
hh:mm:ss.
Box-shaped Cylindrical
M S M S
coarse 00:10:51 15:10:47 00:11:25 14:24:19
Figure 10: Comparison of the box-shaped and the cylindri-
cal simulation domain based on the coarse case. Vertical
sample of
uy
at h
/2
for different mesh sizes. Depicted as
•
is the sample from measurements in the wind tunnel.
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
0 1000 2000 3000 4000 5000
Residual
Iteration
Ux
Uy
Uz
p
omega
k
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
0 1000 2000 3000 4000 5000
Residual
Iteration
Ux
Uy
Uz
p
omega
k
Figure 11: Residuals of box-shaped domain (top) and cylin-
drical domain (bottom).
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DIS CU SS IO N
The results presented show that it is possible to employ a
cylindrical simulation domain for urban CFD simulations.
The residuals of the cylindrical case show that the proposed
approach shows solid convergence behavior which is similar
to conventional box-shaped simulation domains.
Where high-pressure gradients are expected, the mesh has to
be appropriately refined to capture important flow features
and to adequately resolve the boundary layer. Consequently,
for box-shaped domains, one needs higher mesh resolution
around all building geometries as well as at the ground
boundary. A cylindrical domain needs to be created in a way
that flows from all directions can be sufficiently resolved.
Since the building geometries are identical for both cases, a
significant amount of additional cells (21 %) is introduced
at the ground boundary for the cylindrical domain. This
disadvantage is illustrated in figure 9.
The results show that the cylindrical domain shows better
simulation times which is very likely due to the differences
in convergence behavior illustrated in figure 11 — and which
we believe happened coincidentally for this particular case.
Given the higher mesh count of the cylindrical case, the time
per iteration for a cylindrical domain is higher than for a
box-shaped domain. Thus, by extrapolating those iteration
times, one can infer that the only possibility to achieve
faster simulation times than with a cylindrical domain would
be to achieve better convergence behavior, meaning that
fewer iterations will yield the same results. If this is not
the case, a cylindrical simulation domain will always be
at a disadvantage over the box-shaped domain in terms of
simulation time.
Aside from that, the nature of the annual wind analysis
problem warrants another, more holistic comparison: for
this purpose we assume identical convergence behavior and
that every wind direction simulation starts with a ”positive
budget” which equals the meshing time of a corresponding
box-shaped case. This budget, in this case, would be 10 min
and 51 s or 651 s. This budget of 651 s is exhausted after 131
iterations of simulation time for the cylindrical domain. In
other words, the simulation time of the cylindrical domain
may be 651 s longer to still win over the box-shaped case.
By extrapolating both iteration times for
∼
3000 iterations,
we yield a total simulation time of 13.3 and 17.5 h for the
box-shaped and the cylindrical domain respectively. The
fact that the
∆t
of both total times is far greater than
651 s
,
we believe that hardly any considerable time advantages
could be achieved with different mesh densities.
However, the advantages of a cylindrical domain outweigh
the disadvantages in some cases. First, in practice with real
geometries, the scale of most urban CFD simulations sug-
gests to run those overnight or over the weekend. Given
those time-spans, improvements in simulations time are
desirable but only magnitudes in simulation time improve-
ments would change the way of working with such large-
scale simulation cases. On the contrary, incorrect simulation
setups or non-reliable simulation cases might result in a
weekend of lost simulation time.
Aside from differences in meshing time, we would like
to emphasize that CFD simulations are highly sensitive to
the input mesh and its quality. The creation of such high-
quality meshes often requires time-consuming and tedious
preprocessing efforts, mostly for cleaning the geometries.
Considering these efforts, one can make use of the inherent
advantages of a cylindrical simulation domain. In using a
cylindrical domain with a high-quality mesh, one can use it
for all subsequent simulations of different wind directions.
The simulation of each wind direction may be started in par-
allel after one single mesh is created. This possibility might
help to identify problems in the buildings’ design before
one might happen to reach the particular wind direction that
reveals problems with a sequential simulation approach. Fur-
thermore, CFD analysis for the built environment is usually
characterized by iterative design alterations which have been
outlined above. Every design alteration is likely to introduce
new mesh inconsistencies that, for the box-shaped domain,
might elicit meshing issues for every new wind direction
that is required to be studied. In contrast, these hindrances
do not exist for the cylindrical domain. Consequently, one
requirement we see for the further automation of CFD work-
flows in the field of building performance simulation is the
reliability to achieve robust, converging simulation cases.
Apart from mixed polyhedral meshes that were used in this
study, other commonly used meshes include hexahedral-
only, tetrahedral-only meshes. We are aware of the advan-
tages that those might have in terms of accuracy or simula-
tion time. Unfortunately, none of the latter ones have been
implemented in OpenFOAM in a robust manner at the time
of writing this manuscript. As soon as those meshes become
available, the presented cylindrical meshing approach could
take advantage of them.
CON CL US IO N
In this study, we proposed a cylindrical mesh for urban wind
simulations. We showed that cylindrical simulation domains
for urban CFD simulations are feasible with OpenFOAM.
We examined a commonly used validation case for which
we compared the box-shaped computational domain with
the cylindrical simulation domain, both by considering the
best practice dimensions for environmental flows. Meshing
and simulation time comparisons showed that it is recom-
mendable to use the box-shaped approach if no annual wind
analysis is intended. A cylindrical simulation domain is
likely to have advantages over the box-shaped approach
from a methodological standpoint and if further simulations
with the same mesh may be necessary for different wind
directions at a later point in time. In future work, we plan
to validate the results of the urban wind case in a further
study and envision to link the results from the annual wind
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study with Building Energy Simulation software for more
accurate natural ventilation potential estimations.
ACK NOW LE DG ME NT
The authors would like to acknowledge the financial support
by the Cornell University David R. Atkinson Center for a
Sustainable Future and the Cornell Center for Transportation,
Environment, and Community Health which funded this
research.
Nomenclature
ABL atmospheric boundary layer
AFN air flow networks
BC boundary condition
BEM building energy modeling
CAD Computer-aided design
CFD Computational Fluid Dynamics
GCI grid convergence index
NV natural ventilation
RANS Reynolds-averaged Navier-Stokes
SIMPLE
Semi-Implicit Method for Pressure Linked
Equations
SST Shear Stress Transport
WT wind tunnel
cppressure coefficients
hnormalized grid spacing
Cmu constant
turbulence dissipation rate, m2s−3
κvon Karman constant
ppressure, kg m−1 s2
rgrid refinement ratio
R2coefficient of determination
Uvelocity, m s−1
uref reference velocity, ms−1
U∗friction velocity, m s−1
˙vvolumetric flow rate, m3s−1
ωspecific dissipation rate, s−1
yivalues of choice
ˆyipredicted values of choice
¯yimean values of choice
zheight, m
z0surface roughness length, m
zmin min. coordinate value in z-direction, m
zref reference velocity, ms−1
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