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ARTICLE TEMPLATE

A Cylindrical Meshing Methodology for Annual Urban Computational Fluid

Dynamics Simulations

Patrick Kastneraand Timur Dogana

aCornell University, Ithaca, NY, USA

ARTICLE HISTORY

Compiled December 7, 2020

ABSTRACT

For urban CFD simulations, it is considered a best practice to use a box-shaped simulation do-

main. Box-shaped domains, however, show drawbacks for airﬂow from several wind directions

as remeshing and additional preprocessing steps become necessary. We introduce a routine

to create a cylindrical mesh that expedites the simulation of arbitrary wind directions using

OpenFOAM. Results computed with the cylindrical domain are validated against wind tunnel

data. We report that the cylindrical method yields comparable results in terms of accuracy and

convergence behavior. Further, run time comparisons in a real-world scenario are conducted

to discuss its advantages and limitations. Based on the ﬁndings, we recommend using the

cylindrical approach if at least eight wind directions are analyzed for which we report 18 % run

time savings. The cylindrical domain along with automated best practice boundary conditions

has been implemented in Eddy3D — a plugin for Rhinoceros.

KEYWORDS

CFD; urban; meshing; box-shaped; cylindrical; multi-directional

Introduction

Urbanization and population growth, along with a massive predicted construction volume can

be seen as a unique opportunity to improve the built environment and its quality of living

through integrated and well-informed architectural urban design processes. Such processes lead

to high quality, climate-adaptive architecture that uses passive means to provide comfortable

environments with smaller carbon footprints. Not only in Mediterranean countries but also in

countries with subtropical and tropical climates where the largest construction volumes are

expected, natural ventilation (NV) is one of the most eﬃcient ways of cooling and promises a

signiﬁcant energy saving potential. In such regions, studies have shown the possibility of saving

up to

50 %

in energy compared to air conditioning (Cardinale et al., 2003; Oropeza-Perez and

Østergaard, 2014).

Author Email: pk373@cornell.edu

To evaluate such savings, building energy modeling (BEM) packages like EnergyPlus and

TRNSYS come with capable airﬂow network (AFN) solutions for natural ventilation evaluation

in multi-zone building energy models (Huang et al., 1999; Weber et al., 2003). These solutions

rely on pressure coeﬃcient arrays for diﬀerent wind directions and exterior simulation nodes. For

simple box-shaped buildings without contextual obstructions, look-up tables and fast methods

for surface-averaged pressure coeﬃcient generation exist (Grosso, 1992; Swami and Chandra,

1988). Since then, many attempts have been made to deal with airﬂow sheltering eﬀects for

simpliﬁed urban geometries, and there is evolving literature about wind pressure coeﬃcients

for sheltered buildings that are summarized by Costola et al.. For unique geometries, and if

surrounding buildings exist, further attention is needed to avoid geometric oversimpliﬁcation

(Cheung and Liu, 2011). This is especially important when it comes to annual analyses, that

is, analyses for all hours of the year, for which multi-directional CFD simulations are needed.

In these multi-directional conditions, computational ﬂuid dynamics (CFD) analyses are used,

either as a standalone tool or to inform the AFN method with more accurate pressure coeﬃcient

(

𝑐𝑝

) input data. CFD is a numerical methodology to calculate desired ﬂow variables on a lattice

within a simulation domain by solving the Navier-Stokes equations (NSE). The usual steps of a

recurring CFD analysis in a design 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 for multiple

wind directions;

(4)

postprocessing the variables of interest, likely followed by design alterations that lead

back to (1) if goals or constraints have not been met.

The expertise needed to perform such analyses and the associated preprocessing overhead often

impedes a wider use of natural ventilation studies in building and urban scale design workﬂows.

As a result, NV studies are expensive and usually are only undertaken late in the design process

when signiﬁcant changes to improve the NV potential are often no longer feasible. Hence, to

incorporate natural ventilation analyses into early design stages, the workﬂows for annual wind

analysis need to be (1) streamlined, and (2) the time to produce actionable results needs to be

reduced.

In this study, we propose a novel methodology to reduce the preprocessing and simulation time

of annual urban wind simulations by utilizing the CFD library OpenFOAM. For this, we use a

cylindrical simulation domain that allows for a seamless assignment of boundary conditions for

arbitrary wind directions. Further, we discuss meshing issues that might occur when cylindrical

meshes for urban CFD simulations are used. We introduce a robust workﬂow that expedites

annual wind ﬂow analyses that are relevant for applications shown in ﬁgure 1. We investigate

the convergence behavior, accuracy, and run times in two studies:

(1)

In a validation study, we conduct a grid convergence study for four stages of mesh

reﬁnement. Then, we evaluate the accuracy and convergence behavior of both the box-

shaped and cylindrical domains for a reference case by Jiang et al. (2003) from the previous

grid convergence study.

(2)

In a more detailed annual study, we use a square-shaped building array to assess the

diﬀerences to complete both meshing and simulation referred to as run time.

Annual wind

CFD methodology

Urban CAD model

Annual

wind data

Building Performance

Simulation

Scope of

this work

Airflow networks

analysis

cpvalues for every 5°

wind direction increments

Estimation of annual

air change rates

Outdoor thermal

comfort analysis

Air velocities at

high spatial resolution

Pedestrian wind

comfort analysis

Figure 1.: Collocation scheme of the investigated approach within the urban simulation process.

Background

When it comes to spatial analysis and decision aiding for the built environment with CFD,

particular attention should be paid to meshing methodologies. Several best practice guidelines

for urban ﬂow problems have been published over the years (Franke et al., 2004; Franke,

2006; Franke and Baklanov, 2007; Franke et al., 2010; Tominaga et al., 2008; Blocken,

2015; Ramponi and Blocken, 2012), all of which propose best practices concerning domain

dimensions, convergence criteria, and relaxation factors. Little focus, however, has been put on

how to best approach the meshing of a simulation domain for annual wind simulations.

For urban CFD simulations that take into account a single wind direction, it is considered best

practice to construct a box-shaped wind tunnel (WT) with predeﬁned dimensions in relation

to the building geometry. A commonly-used practice proposed by Tominaga et al. suggests a

simulation domain size of

𝑧=6·𝐻𝑚𝑎 𝑥

,

𝑙=20 ·𝐻𝑚𝑎 𝑥

and

𝑤

given a blocking ratio of

≤3 %

,

where

𝑧

,

𝑙

, and

𝑤

are the dimensions of the simulation domain and

𝐻𝑚𝑎 𝑥

is the height of the

tallest building in the building agglomeration. The blocking ratio is deﬁned as the ratio between

the projected facade area of the buildings perpendicular to the inlet to the total area of the inlet

in wind direction.

There are two approaches to account for diﬀerent wind directions: one may either rotate the

building geometry that is placed in the simulation domain (ﬁgure 2 (a)), or set up an entirely

new simulation domain with corresponding boundary conditions for each additional wind

direction (ﬁgure 2 (b)). In each subﬁgure, the dashed lines represent the wind tunnels and

wind directions after an arbitrary rotation. Both options come with disadvantages. In the ﬁrst

case, the entire simulation domain needs to be remeshed for every additional wind direction.

However, as the height of the WT depends on a constant

𝐻𝑚𝑎 𝑥

, a change in the windward-facing

projected facade area introduced by rotation, results in a diﬀerent width of the WT. In manual

preprocessing setups, width adjustments for adequate blocking ratios are often neglected. As

a result, the same WT width is used for all wind directions, which may lead to convergence

problems (ﬁgure 2 (a)). For the second approach shown in ﬁgure 2 (b), the coordinates of

the WT and the boundary conditions need to be adjusted to account for changes in wind

directions, thus likely violating the best practice dimensions for the WT width if omitted.

Hence, box-shaped simulation domains show drawbacks when many wind directions need to

be simulated because of the given climate data. While (re)meshing of single, exposed building

geometries for few wind directions is manageable, more involved problems (many directions

with surrounding urban context) become increasingly complex to handle.

(a) (b)

Figure 2.: Top view of simulation domains to account for diﬀerent wind directions.

To avoid the creation of a new mesh for every wind direction, we propose a cylindrical

computational mesh that allows for a streamlined simulation of arbitrary wind directions,

see Case C and C’ in ﬁgure 3. Further, the setup of boundary conditions is automated such

that a signiﬁcant amount of time will be saved for the setup of an annual wind analysis (up

to 32 or more wind directions). More speciﬁcally, every lateral cylinder patch represents

an individually deﬁned angular increment and can be assigned to either an inlet or outlet

boundary condition depending on the particular wind direction (ﬁgure 4). Moreover, the angular

increment determines the block size of the inner rectangle. This makes the same mesh reusable

for the simulation of any arbitrary wind direction. Case A and A’ in ﬁgure 3 illustrate the

box-shaped wind tunnel, whereas Case B/B’ and C/C’ illustrate a square-shaped and cylindrical

simulation domain, each of them with best practice dimensions imposed. Little is known

about cylindrical meshes for this purpose, hence, a thorough study of accuracy, convergence

behaviors, and actual computational speed gains are required.

Methodology

Validation study

This section consists of two analyses: ﬁrst, we conducted a grid independence study for a

box-shaped domain for a single wind direction and a single building geometry. With the

suﬃciently-reﬁned grid, we compared its accuracy and convergence behavior to a mesh

Case A Case B Case C

15 Hmax

Hmax

5 Hmax

s.t. blocking ratio = 3 %

6 Hmax

15 Hmax

15 Hmax

Building geometries

inlet

outlet

15 Hmax

15 Hmax

Projected

facade area

Top vi ew Front vi ew Top vi ew Front view

Case A’ Case B’ Case C’

15 Hmax

Hmax

5 Hmax

s.t. blocking ratio = 3 %

6 Hmax

15 Hmax

15 Hmax

Building geometries

inlet

outlet

15 Hmax

15 Hmax

Projected

facade area

Top vi ew Front vi ew Top vi ew Front view

Figure 3.: Top row: top views of the simulation domain for an arbitrary urban area; Case A

shows a conventional simulation domain, Case B shows a square-shaped simulation domain,

and Case C shows a cylindrical simulation domain, each for a wind direction of 0

°

. Bottom

row: Cases A’-C’ for wind directions of 45°. The illustrations are not true to scale.

produced with the cylindrical approach.

Jiang et al. (2003) conducted an extensive study in an atmospheric boundary layer (ABL) WT

in which a cuboid with two openings had been investigated experimentally to estimate the

cross-ventilation behavior (ﬁgure 5).

The geometry in ﬁgure 5 (a) was modelled in

Rhinoceros

with inﬁnitely thin walls, neglecting

the

6 mm

wall thickness of the scale model. The Grasshopper plugin Eddy3D was used to

automate the preprocessing, including the assignment of boundary conditions. The mesh

was created by using the blockMesh utility for the background mesh and snappyHexMesh to

subsequently snap the background mesh to the building geometry, producing a mixed polyhedral

mesh. The dimensions of the box-shaped simulation domain are

(5.75 ·2.75 ·1.5) m

. When

using a cylindrical mesh, while ensuring not to violate the best practice dimensions for length,

width, and height, the ground area of the mesh is larger. It is characterized by a higher cell

count than one would anticipate with the conventional approach shown in ﬁgure 3 for Case A.

To ensure a fair comparison between both approaches, we created the blockMesh with identical

Lateral patch

Angular

increment

Cylindrical patches

with inlets/outlets

imposed

Figure 4.: Top view of the lateral cylinder patches. A coarse setting is shown left, a substantially

ﬁner mesh is shown on the right.

(a) (b)

h = 0.25 m

h/2

0 h

Figure 5.: (a) Schematic of the validation wind tunnel geometry; (b) Vertical section through

validation domain with geometry spanning from 0to ℎ.

cell sizes in the areas where the buildings were placed and used identical mesh reﬁnement

levels. Figure 6 illustrates both the box-shaped and the cylindrical domains considering best

practice guidelines as they were created in Grasshopper. In this example, the lateral patches of

the cylindrical domain consist of 5°straight line segments.

The domain inlet was set to an atmospheric boundary layer proﬁle for

𝑈

,

𝑘

, and

𝜔

. At the

outlet of the computational domain, constant pressure is assumed, while the other variables

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 pressure, and wall

functions for

𝑘

and

𝜔

. For

𝜈𝑡

, the intelligent wall function called nutUSpaldingWallFunction

was used. The front, back, and top faces are set to symmetric boundary conditions for all

variables. The kinematic viscosity,

𝜈

, was set to

1.5 ×10−5

. The turbulence inlet parameters

were calculated using the following equations:

𝑘=(𝑈∗)2

√𝐶𝑚𝑢

(1)

𝜀=(𝑈∗)3

𝜅(𝑧+𝑧0)(2)

𝜔=

𝜀

𝐶𝑚𝑢 ·𝑘(3)

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 6.: 3D visualization of box-shaped wind tunnel (WT) and cylindrical WT.

where

𝑈∗

is the friction velocity, and

𝐶𝑚𝑢 =0.09

is a constant for the turbulence model. The

values used are summarized in table 1.

Table 1.: Turbulence boundary conditions used for the validation study.

Parameter Value

𝑘0.034 56

𝜖0.0835

𝜔10.42

The approach to model the ABL in OpenFOAM is based on the following equations (Wallace

and Hobbs, 2006):

𝑈=

𝑈∗

𝜅𝑙𝑛 𝑧+𝑧0

𝑧0(4)

𝑈∗=𝜅𝑈𝑟 𝑒 𝑓

𝑙𝑛 𝑧𝑟 𝑒 𝑓 +𝑧0

𝑧0(5)

where

𝑈∗

is the friction velocity,

𝜅

is the von Karman constant,

𝑈𝑟 𝑒 𝑓

is the reference velocity

at the reference height

𝑧𝑟 𝑒 𝑓

, and

𝑧0

is the aerodynamic roughness length. In the original

experiment, the atmospheric boundary layer proﬁle of the WT’s inlet velocity 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 of the resulting

𝑧0

, hence, a value of

𝑧0=

0.005 m

has been used in this study. All numerical simulations are based on OpenFOAM’s

steady-state simpleFoam solver in combination with a

𝑘−𝑤−𝑆𝑆𝑇

RANS turbulence model.

The pressure-velocity coupling was established with the SIMPLE algorithm using three

non-orthogonal corrector loops. 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

1×10−4f

or

𝑝

and

1×10−5f

or the

remaining ﬁelds. For each case, we simulated until the convergence criteria were reached. The

relaxation factors were chosen to be

0.7

for

𝑝

and

0.3

for

𝑈

,

𝑘

and

𝜔

. All simulations ran 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 OpenFOAM 4.1. At most, we ran a maximum

of four OpenFOAM instances at a time on single CPUs on separate threads to avoid aﬀecting

the run times by other processes. All other values including the discretization schemes not

speciﬁcally mentioned here were selected according to current best practice guidelines (Franke,

2006).

To compare the OpenFOAM results of both meshing methodologies against the WT data,

measurements by Jiang et al. (2003) were digitized and subsequently interpolated to yield

50 sampling points. The axes were normalized by

ℎ=0.25 m

and

𝑢𝑟 𝑒 𝑓 =12 m s−1

. For

later comparison, vertical, stream-wise velocity measurements were taken at

ℎ

2

, as the largest

deviation from the measured data was found there, see ﬁgure 5. First, the results for the

reﬁnement study were sampled with the sample utility using the cellPoint interpolation scheme

in OpenFOAM, which is a linear-weighted interpolation using cell values. The sampled results

were then plotted against the experimental data and the coeﬃcient of determination (

𝑅2

) was

calculated:

𝑅2=1−Í𝑁

𝑖=1(𝑦𝑖−ˆ𝑦𝑖)2

Í𝑁

𝑖=1(𝑦𝑖−¯𝑦𝑖)2,with 0≤𝑅2≤1(6)

To verify and report grid independence, reﬁned meshes were created by increasing the number

of divisions of the background mesh by factors of two in each Cartesian direction while keeping

the levels of surface and feature reﬁnements constant. To provide a standard and consistent

approach to report the results of grid convergence studies (GCS) and error estimations, we

adopted the concept of the grid convergence index (GCI) by Roache which is based on a derived

variable. The derived variable, in our case, is the volumetric ﬂow rate through the opening.

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 by further reﬁning the grid. Moreover, we use Richardson

Extrapolation (RE) to predict the ﬂow rate for an ideal mesh (continuum), thereby estimating

the magnitude of the numerical error. The mesh size for each reﬁnement stage is summarized

in table 2, and the meshes themselves are illustrated in ﬁgure 7.

Annual study

A previous study found that a singled out, cubic building geometry is not adequate to highlight

the beneﬁts of the proposed method in terms of overall run times (Kastner and Dogan, 2018). To

establish a more real-world-like scenario, we created simulation domains for a square-shaped,

equidistant building array consisting of cubes with a

20 m

edge length. To ensure a fair

comparison between the meshes, the reﬁned regions in the center of the simulation domain are

identical and the surrounding coarser regions were set up with the same cell divisions. For

this study,

𝑢𝑟 𝑒 𝑓

was arbitrarily chosen to be

5 m s−1

and the turbulence values were calculated

according to equation 1 - 3.

The Cases A and A’ exemplify a rotation of the simulation domain (0

°

and 45

°

representing the

two extremes in terms of the projected facade area) according to the best practice rules if the

blocking ratio is ﬁxed at

3 %

. This leads to an increase in the size of the simulation domain

for Case A’. By simulating these two extreme cases, a full 360

°

study is reproduced with 45

°

stepwise rotations by exploiting the rotational symmetry of A and A’. Moreover, we assessed

a square-shaped simulation domain suggested by Franke and Baklanov (Case B), which is

characterized by automatically-generated inlet and outlet boundary conditions identical to Case

C. This approach, often used as a workaround for expedited case setups, also beneﬁts from

only having to be meshed once no matter which wind direction is imposed. Finally, Case C

represents the cylindrical approach that we propose in this study. To estimate the ﬁnal run times

of a set of hypothetical wind directions, we summed up the meshing and simulation times and

multiplied them by the corresponding number of wind directions (or rotations). Hence, the

meshing time was taken into account multiple times for Case A and A’, whereas only a single

time for Case B and C.

Results

Validation study

(a) very coarse (b) coarse (c) normal (d) ﬁne

Figure 7.: Excerpt of reﬁned mesh sizes for the validation study.

Figure 7 shows a cropped stream-wise section around the building geometry for each mesh

reﬁnement. For each of the meshes, the vertical velocity samples are depicted in ﬁgure 8,

in which the normalized domain height is plotted over the normalized reference velocity

𝑢𝑦

.

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, under-predicts the normalized velocity,

especially in the opening region.

0.50 0.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50

uy

uref [ ]

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

z

h[ ]

Wind tunnel

Boxvery coarse,

R

2= 0.921

Boxcoarse,

R

2= 0.946

Boxnormal,

R

2= 0.962

Boxfine,

R

2= 0.952

Figure 8.: Coeﬃcients of determination (

𝑅2

) for vertical velocity probes

𝑢𝑦

at

ℎ

2

for diﬀerent

mesh sizes.

In the experiment conducted by Jiang et al. (2003), a volumetric ﬂow rate of

0.045 m3s−1

was

measured for the opening of the building geometry. Contrary to the vertical velocity probes, all

stages of the grid reﬁnement conﬁrm the measurement of that derived variable in a converging

manner toward the ﬁner grids (ﬁgure 9 and table 2). By evaluating the GCS, the volumetric ﬂow

rate for an ideal mesh would be

0.047 m3s−1

, which is in good agreement with the experimental

results of

0.045 m3s−1

. Furthermore, the ratios of the CGIs conﬁrm that the volumetric ﬂow

rates reported in the GCS are well within the asymptotic range of convergence (Kastner, 2016).

Given the reasonable numerical error band of

∼10 %

, we decided to continue with the “coarse”

grid for the subsequent accuracy comparison.

Table 2.: Parameters of the grid convergence study for four diﬀerent mesh sizes: very coarse,

coarse, normal, and ﬁne.

Case Cell count ℎ𝑔𝑟¤𝑣[m3s−1] Error (experiment) Error (continuum) GCI [%]

very coarse 124 456 8 1.3 0.0540 17 % 15 % 11.04

coarse 263 919 4 1.6 0.0505 11 % 10 % 6.82

normal 1 165 733 2 1.6 0.0485 7% 6 % 4.94

ﬁne 4 940 280 1 - 0.0471 4 % 3 % -

RE - 0 - 0.0456 - - -

Experiment - - - 0.0450 - - -

To compare the accuracy of the box-shaped and the cylindrical method, the vertical, stream-wise

probes

𝑢𝑦

are plotted at

ℎ

2

, for the “coarse” mesh setting, see ﬁgure 10. It is evident that the

012345678

Normalized grid spacing (h) [ ]

0.045

0.046

0.047

0.048

0.049

0.050

0.051

0.052

0.053

0.054

Volumentric flow rate [m3/s]

v (

h

= 8, 4, 2)

v (

h

= 0, RE)

Not considered for RE

Experiment

Figure 9.: Richardson Extrapolation (RE) of the volumetric ﬂow rate

¤𝑣

through the windward

opening based on the grid convergence study.

box-shaped simulation domain achieves a marginally higher

1

accuracy (

𝑅2=96.7 %

) than

the cylindrical simulation domain (

𝑅2=94.1 %

). However, both approaches either under-

and/or overestimate regions with high-pressure gradients which is known as a deﬁciency of the

steady-state RANS model.

0.50 0.25 0.00 0.25 0.50 0.75 1.00 1.25 1.50

uy

uref [ ]

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

z

h[ ]

Wind tunnel

Cylinder,

R

2= 0.94

Box,

R

2= 0.97

Figure 10.: Vertical sample

𝑢𝑦

at

ℎ

2

for the box-shaped and the cylindrical simulation domain.

Figure 11 depicts the residuals reported for both cases. Here, the cylindrical domain shows

better convergence behavior for the particular convergence criteria (ﬁgure 11 (b)). This results

1

The marginally higher

𝑅2

(

94.6 %

vs.

96.7 %

) in ﬁgure 10 vs. ﬁgure 8 stems from using three additional mesh boundary layers

for the ground and the building surfaces.

in a simulation that converges after

∼2900

iterations for the cylindrical case, whereas the

box-shaped WT converges after ∼4100 iterations.

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

(a) (b)

Figure 11.: Residuals of box-shaped (a) and cylindrical simulation domain (b).

Annual study

The annual study is concerned with evaluating the run times for a square-shaped, equidistant

building array. The top row in ﬁgure 12 shows the top view of the meshes after the blockMesh

routine in OpenFOAM. A detailed summary of the three simulation domains is given in table 3.

For Case A/A’, the width of the WT varies with the angle of the approaching wind (which is

largest in the particular Case A’) due to the constraint to keep the blocking ratio constant. The

bottom row in ﬁgure 12 shows horizontal velocity plots at

2 m

above the ground plane. This

conﬁrms visually that all simulation domains are comparable in capturing the ﬂow ﬁeld, as

shown before.

Figure 13 provides an extrapolation of the individual meshing and simulation time for an annual

analysis of an urban area depending on the number of wind directions. For the individual

meshing times, we report a signiﬁcantly higher meshing time for Case A’ compared to the three

other cases. The extrapolation in ﬁgure 13 reveals that the cylindrical simulation domain (Case

C) yields

18 %

better run times compared to the conventional approach (Case A/A’) if 8 or

more wind directions are simulated. Moreover, Case C shows

39 %

better overall run times

compared to the square-shaped approach (Case B) regardless of the number of wind directions.

Table 3.: Geometry and mesh information about the cases A, A’, B, and C.

Case Dimensions Mesh

In ﬂow

direction [𝑚]⊥to ﬂow

direction [𝑚]

Ground area

[𝑚2]

Projected facade

area [𝑚2]

Cell count Cells per ground

area [𝑐𝑒𝑙𝑙𝑠/𝑚2]

A 1.200 399 4.79E+05 4.000 8.1E+05 1.69

A’ 1.200 1.408 1.69E+06 10.182 1.4E+06 0.83

B/B’ 1.600 1.600 2.56E+06 10.182 1.3E+06 0.51

C/C’ 1.600 1.600 2.01E+06 10.182 9.7E+05 0.48

Case A Case A’ Case B’ Case C’

Figure 12.: Top row: meshes after the blockMesh routine. Case A and A’ correspond to a

box-shaped tunnel for 0 and 45

°

, Case B’ corresponds to a square-shaped approach, and Case

C’ corresponds to a cylindrical approach. Bottom row: horizontal velocity plots at 2 m above

the ground plane.

Discussion

The results show that it is possible and beneﬁcial to employ a cylindrical mesh for annual/multi-

directional urban CFD simulations with OpenFOAM. Where high-pressure gradients are

expected in the simulation domain, the mesh has to be appropriately reﬁned to capture

important ﬂow features and to adequately resolve the boundary layer. We estimated the

numerical error resulting from our validation mesh setting to be

∼10 %

with the help of a grid

convergence study (GCS). GCSs for large meshes are not a trivial task, as the simulation time

grows exponentially with the number of background mesh divisions. However, this method is

useful to both estimate the numerical error and to conﬁrm an adequate convergence behavior

0

500

1000

1500

2000

2500

3000

1 2 4 8 16 32

Time [min]

Number of wind directions

A/A'

B/B'

C/C'

Case Time [min]

Meshing Simulation

A 2.2 47.0

A’ 11.4 60.7

B/B’ 3.5 81.0

C/C’ 2.3 49.7

.

Figure 13.: Meshing and simulation times for cases A/A’, B/B’, and C/C’

by utilizing a reasonable number of mesh reﬁnements. To put this eﬀort into perspective, we

would like to emphasize that this study focuses on the comparison of two diﬀerent meshing

approaches, not to achieve the best overall accuracy. Here, the GCS conﬁrms that the reﬁnement

strategy follows commonly-accepted guidelines and that the coarse mesh is suﬃcient for the

goals of this study.

Further, we show that for the coarse mesh, the box-shaped simulation domain achieves a

marginally better accuracy

(𝑅2=96.7 %)

than the cylindrical simulation domain

(𝑅2=94.1 %)

while both domains either under- and/or overestimate regions with high-pressure gradients.

The deﬁciency in accuracy in high-pressure regions can be attributed to the steady-state RANS

model. While we are aware of the limited applicability of the RANS approach for urban ﬂows,

it is noteworthy that the application of the method proposed in this study focuses on early

design exploration for the built environment. Thus, we emphasize the interest in overall feasible

run times rather than accuracy. However, the cylindrical meshing approach presented can be

used independently of the solver. Therefore, such deﬁciencies could be avoided by using more

advanced LES or DNS solvers, should the need for very accurate results arise.

In ﬁgure 13, we summarize the run time comparisons for an annual analysis with multiple

wind directions that are extrapolated from the individual meshing and simulation times. Here,

the run times reported for Case A and A’ were linearly interpolated to estimate the theoretical

run times in the case of 16 and 32 wind directions and the necessary rotations. For Case A

and A’, it is suﬃcient to adhere to the best practice dimensions from the wind direction of that

simulation instance (either

0°

or

45°

), whereas a cylindrical domain needs to be created in

a way that wind from all directions can be simulated appropriately. Hence, additional cells

are introduced at the ground surface of the cylindrical domain, see ﬁgure 6. Considering that

trade-oﬀ, we suggest that simulation domains according to Case A/A’ be used for analyses with

<

8 wind directions

2

. For

≥

8 wind directions, the fact that the cylindrical domain only needs

to be meshed once makes up for the additional number of cells in the simulation domain. Thus,

for ≥8 wind directions, we suggest using the cylindrical approach.

However, it should be emphasized that the advantages of a cylindrical domain may outweigh

the disadvantages even in cases with fewer than 8 wind directions as CFD simulations are

highly sensitive to the quality of the CAD input geometry. First, in practical use with real-

world problems, the scale of most urban geometries suggest overnight or over-the-weekend

simulations. Given these time-spans, improvements in simulations time are indeed desirable

but only magnitudes in run time improvements would change the way of working with such

large-scale simulations. On the contrary, malfunctioning simulation setups that stem from

manually changing the boundary conditions might result in weekends of wasted computing

time. Furthermore, the creation of robust, high-quality meshes often requires time-consuming

and tedious preprocessing eﬀorts, mostly for cleaning the CAD geometries. CFD analyses

for the built environment are usually characterized by iterative design changes that have been

2

In an earlier study, a less optimistic result had been reported which neglected the eﬀect that the rotation enforces by increasing

the width of the WT while keeping the blocking ratio constant (Kastner and Dogan, 2018).

outlined above. Every change is likely to introduce new mesh inconsistencies that, for Case

A and A’, might elicit meshing or convergence issues for every additional wind direction.

Considering these impediments, we suggest making use of the inherent advantages of a

cylindrical simulation domain. Here, the simulation domain only needs to be validated once,

which subsequently guarantees valid simulation results from all directions. Moreover, the

simulations for all wind directions may even be started in parallel after the single mesh is

created. This possibility might help to identify problems in a buildings’ design early on before it

might be discovered with a sequential simulation approach. Consequently, one requirement we

see for the prospective automation of CFD workﬂows for the built environment is the ability to

produce robust, converging simulation cases. As a ﬁrst step in that direction, we suggest using

a cylindrical simulation domain if the meshing process of the particular building geometry

seems to be unstable and likely to fail in the case of further geometry rotations.

Apart from mixed polyhedral meshes that were used in this study, other commonly used meshes

include hexahedral-only, tetrahedral-only meshes. As the two latter are known to achieve

better performance in terms of meshing time, future work should investigate whether such

an approach might aﬀect the conclusions drawn. From an implementation perspective, the

cylindrical meshing approach could take advantage of faster meshing times.

In future work, we plan to use the results from such annual wind studies as input for BEM

software to inform the prediction of the natural ventilation potential of buildings.

Conclusion

In this study, we propose a cylindrical mesh for urban wind simulations and show that such

simulation domains are feasible and beneﬁcial with OpenFOAM. We examined a commonly-

used validation case for which we compared the box-shaped computational domain to the

cylindrical simulation domain while considering best practice dimensions for urban CFD

studies. Meshing and simulation time comparisons show that it is recommended to use the

box-shaped approach if fewer than 8 wind directions are intended to be studied. We show

that the cylindrical simulation domain shows better overall run times in the case of 8 or more

wind directions. Concluding, we discuss how a cylindrical simulation domain may likely have

advantages over the box-shaped approach from a methodological perspective, even if fewer

than 8 wind directions are studied.

Acknowledgment

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

DNS Direct numerical simulation

GCI Grid convergence index

GCS Grid convergence study

NV Natural ventilation

LES Large eddy simulation

RANS Reynolds-averaged Navier-Stokes

SIMPLE Semi-Implicit Method for Pressure Linked Equations

SST Shear stress transport

WT Wind tunnel

𝑐𝑝Pressure coeﬃcients

ℎHeight, m

ℎ𝑔Normalized grid spacing

𝐶𝑚𝑢 Constant

𝜖Rate of dissipation of turbulence energy, m2s−3

𝑘Turbulence kinetic energy, m2s−2

𝜅von Karman constant

𝑝Pressure, kg m−1s2

𝑟Grid reﬁnement ratio

𝑅2Coeﬃcient of determination

𝑈Velocity, m s−1

𝑢𝑟 𝑒 𝑓 Reference velocity, m s−1

𝑈∗Friction velocity, m s−1

¤𝑣Volumetric ﬂow rate, m3s−1

𝜔Speciﬁc dissipation rate, s−1

ˆ𝑦𝑖Predicted values

¯𝑦𝑖Mean values

𝑧Dimensions along z-axis, m

𝑧0Surface roughness length, m

𝑧𝑟 𝑒 𝑓 Reference velocity, m s−1

References

Blocken, B. (2015). Computational ﬂuid dynamics for urban physics : Importance , scales ,

possibilities , limitations and ten tips and tricks towards accurate and reliable simulations.

Building and Environment 91, 219–245.

Boulard, T., J. Meneses, M. Mermier, and G. Papadakis (1996). The mechanisms involved in

the natural ventilation of greenhouses. Agricultural and Forest Meteorology 79(1-2), 61–77.

Cardinale, N., M. Micucci, and F. Ruggiero (2003). Analysis of energy saving using natural

ventilation in a traditional italian building. Energy and Buildings 35(2), 153 – 159.

Cheung, J. O. P. and C. H. Liu (2011). CFD simulations of natural ventilation behaviour in

high-rise buildings in regular and staggered arrangements at various spacings. Energy and

Buildings 43(5), 1149–1158.

Costola, D., B. Blocken, and J. Hensen (2009). Overview of pressure coeﬃcient data in

building energy simulation and airﬂow network programs. Building and Environment 44(10),

2027–2036.

Franke, J. (2006). Recommendations of the COST action C14 on the use of CFD in predicting

pedestrian wind environment. In The Fourth International Symposium on Computational

Wind Engineering, pp. 529–532.

Franke, J. and A. Baklanov (2007). Best practice guideline for the CFD simulation of ﬂows in

the urban environment: COST action 732 quality assurance and improvement of microscale

meteorological models. University of Hamburg.

Franke, J., A. Hellsten, H. Schlünzen, and B. Carissimo (2010). The Best Practise Guideline

for the CFD simulation of ﬂows in the urban environment : an outcome of COST 732. In The

Fifth International Symposium on Computational Wind Engineering (CWE2010), Chapel

Hill, pp. 1–10.

Franke, J., C. Hirsch, A. G. Jensen, H. Krus, M. Schatzmann, P. S. W. Miles, S. D., J. A. Wisse,

and N. G. Wright (2004). Recommendations on the Use of CFD in Wind Engineering.

Technical report, Joint publication.

Grosso, M. (1992). Wind pressure distribution around buildings: a parametrical model. Energy

and Buildings 18(2), 101–131.

Huang, J., F. Winkelmann, and F. Buhl (1999). Linking the COMIS Multizone Airﬂow Model

with the EnergyPlus.

Jiang, Y., D. Alexander, H. Jenkins, R. Arthur, and Q. Chen (2003). Natural ventilation

in buildings: Measurement in a wind tunnel and numerical simulation with large-eddy

simulation. Journal of Wind Engineering and Industrial Aerodynamics 91(3), 331–353.

Kastner, P. (2016). Customizing OpenFOAM to assess wind-induced natural ventilation

potential of classrooms: A case study for BRAC University. Master’s thesis, Technische

Universität München.

Kastner, P. and T. Dogan (2018). Streamlining meshing methodologies for annual urban CFD

simulations. In eSim 2018.

Oropeza-Perez, I. and P. A. Østergaard (2014). Energy saving potential of utilizing natural

ventilation under warm conditions – a case study of mexico. Applied Energy 130, 20 – 32.

Ramponi, R. and B. Blocken (2012). CFD simulation of cross-ventilation for a generic isolated

building: Impact of computational parameters. Building and Environment 53(0), 34–48.

Roache, P. J. (1994). Perspective: A Method for Uniform Reporting of Grid Reﬁnement Studies.

Journal of Fluids Engineering 116(3), 405.

Swami, M. and S. Chandra (1988). Correlations for pressure distribution on buildings and

calculation of natural-ventilation airﬂow. ASHRAE transactions 94(3112), 243–266.

Tecle, A., G. T. Bitsuamlak, and T. E. Jiru (2013). Wind-driven natural ventilation in a low-rise

building: A Boundary Layer Wind Tunnel study. Building and Environment 59, 275–289.

Tominaga, Y., A. Mochida, R. Yoshie, H. Kataoka, T. Nozu, M. Yoshikawa, and T. Shirasawa

(2008). AIJ guidelines for practical applications of CFD to pedestrian wind environment

around buildings. Journal of Wind Engineering and Industrial Aerodynamics 96(10-11),

1749–1761.

Wallace, J. M. and P. V. Hobbs (2006). Atmospheric Science: An Introductory Survey (2 ed.).

Academic Press.

Weber, A., M. Koschenz, V. Dorer, M. Hiller, and S. Holst (2003). TRNFLOW, a new tool for

the modelling of heat, air and pollutant transport in buildings within TRNSYS.