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Stud
y of
Pol
luta
nt D
ispe
rsio
n in
Urb
an E
nviro
nmen
t
Car
bune
scu
Raz
van
Cor
neliu
03/1
6/20
07
Pres
ente
d at
LA
S 20
07
Intr
od
uct
ion
•Pro
ble
m:
The
relia
ble
pre
dic
tion o
f dis
per
sion o
f fl
uid
s re
pre
senti
ng c
hem
ical
or
pollu
tant
com
pound
s has
bec
om
e a
very
im
port
ant
envi
ronm
enta
l as
wel
l as
dai
ly lif
e pro
ble
m
•M
eth
od
olo
gy
: C
om
puta
tional
Flu
id D
ynam
ics
(CFD
) is
the
use
of
com
pute
r si
mula
tions
and p
redic
tions
to b
ette
r under
stan
d p
roce
sses
of
fluid
dyn
amic
s an
d f
low
phen
om
ena
•T
ool:
Cac
tus
is t
he
fram
ework
whic
h w
as u
sed
to im
ple
men
t th
is r
esea
rch p
roble
m.
This
stu
dy
add
s to
and
enhan
ces
the
pre
viousl
y ex
isti
ng
Cac
tus
CFD
Toolk
it
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Poll
uta
nt
Dis
pers
ion
•A
im:
info
rmat
ion a
bout
flow
pat
tern
s/dyn
amic
s an
d
tran
sport
of
conta
min
ants
that
could
hel
p in p
reve
nti
ng
acci
den
ts o
r in
tenti
onal
/ter
rori
st p
lots
in o
rder
to lim
it/a
void
dam
age
to p
erso
ns,
pro
per
ty a
nd
nat
ure
•M
eth
od
olo
gy
: use
CFD
sim
ula
tions
bec
ause
they
are
much
m
ore
cost
-eff
icie
nt
exp
erim
ents
req
uir
ing o
nly
com
pute
r ti
me
vers
us
exp
erim
enta
l te
sts
that
req
uir
e ex
tensi
ve p
repar
atio
n
for
larg
er c
ases
•R
ati
on
ale
: use
CFD
sim
ula
tions
bec
ause
of
the
nee
d t
o
sim
ula
te e
xtre
me c
ase
sth
at c
an n
ot
be
mod
eled
in r
eal-lif
e bec
ause
of
the
leve
l of
com
ple
xit
y or
org
aniz
atio
n t
hat
they
m
ay r
equir
e
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Tools
: C
act
us
•is
an o
pen
-sourc
e, s
cala
ble
, port
able
, in
terd
isci
plin
ary
fram
ework
dev
eloped
at
CC
T-L
SU.
A f
ram
ework
is
a def
ined
su
pp
ort
str
uct
ure
in w
hic
h a
noth
er s
oft
war
e pro
ject
can
be
org
aniz
ed a
nd d
evel
oped
. (w
ikip
edia
def
init
ion)
(htt
p:/
/ww
w.c
actu
scod
e.org
)
•th
e C
actu
s C
FD T
oolk
it w
as
dev
elop
ed a
round
the
gen
eral
idea
of
the
nee
d f
or
a re
liable
C
FD p
latf
orm
to t
ackl
e th
e
mult
itude
of
CFD
ap
plic
atio
ns
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Govern
ing
Eq
uati
on
s
•T
he
evolu
tion o
f th
e C
FD p
roble
m is
done
by
solv
ing t
he
Nav
ier-
Stoke
s eq
uat
ion w
hic
h is
the
PDE
that
fully
des
crib
es
the
mom
entu
m c
onse
rvat
ion o
f N
ewto
nia
n f
luid
s
•Si
nce
we
are
dea
ling
wit
h inco
mpre
ssib
le f
luid
wit
h n
o
forc
ing
ter
m t
he
equat
ion c
an b
e fu
rther
sim
plif
ied t
o:
•T
he
pollu
tant
is m
od
eled
by
a pas
sive
sca
lar
tran
sport
eq
uat
ion:
2
2
Re
1
jj
jx
Scx
ut
∂∂=
∂∂+
∂∂φ
φφ
2
2
Re1
ji
iji
ji
xuxp
xuu
tu∂∂
+∂∂
−=
∂∂+
∂∂
∂∂∂
+∂∂
+∂∂
−=
∂∂+
∂∂
ji
j
ji
ii
jij
i
xxu
xuxP
fxu
utu
2
2
2
31µ
ρρSt
udy
of P
olluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Meth
od
olo
gy
The
pre
ssure
fie
ld d
oes
not
hav
e an
y ex
plic
it e
volu
tion e
quat
ion;
ther
efore
anoth
er w
ay o
f ca
lcula
ting
the
pre
ssure
gra
die
nt
and
the
pre
ssure
fie
ld m
ust
be
use
d (
the
frac
tional
-ste
p p
roce
dure
)
n in i
n in i
DC
tu
u+
=∆
−+2/1
Cal
cula
te a
n inte
rmed
iate
vel
oci
ty f
ield
by
dro
pp
ing t
he
pre
ssure
ter
m in t
he
mo
men
tum
eq
uat
ions
tup
n i ∆⋅∇
=∇
+2/1
2C
alcu
lati
on o
f p
ress
ure
by
an G
auss
-Sie
del
SOR
al
gori
thm
ptu
un i
n i−∇
=∆−
++
2/11
Up
dat
e n
ew v
eloci
ty (
ensu
res
mas
s co
nse
rvat
ion)
01
1
=⋅
∇
∇−
+=
∆−
+
+
n i
n in i
n in i
u
pD
Ctu
u
that
such
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Mark
er
an
d C
ell
(M
AC
) m
eth
od
•M
arke
r an
d C
ell (M
AC
) re
pre
sents
a s
pec
ific
way
of
stori
ng
the
pre
ssure
and
the
velo
citi
es o
n a
com
puta
tional
cel
l
•In
the
MA
C m
ethod,
solu
tion f
ield
s ar
e
not
spec
ifie
d a
t th
e sa
me
loca
tion
(cel
l ce
nte
r) b
ut
rath
er t
he
velo
citi
es a
re
stag
ger
ed h
alf
cell-
wid
th in e
ach
dir
ecti
on w
.r.t
. th
e pre
ssure
•T
his
allo
ws
for
incr
ease
d a
ccura
cy
wit
h s
imple
dis
cret
izat
ion s
chem
es
Pres
sure
x-v
eloci
ty
y-ve
loci
ty
z-ve
loci
ty
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Nu
meri
cal
Dis
creti
zati
on
s
•th
e te
mpora
l te
rm is
dis
cret
ized
wit
h a
sim
ple
bac
kwar
d
schem
e
•th
e dif
fusi
on t
erm
s ar
e d
iscr
etiz
ed b
y a
seco
nd
ord
er
accu
rate
cen
tral
dif
fere
nce
sch
eme
•th
e pre
ssure
gra
die
nt
term
s ar
e ca
lcula
ted
usi
ng a
cen
tral
dif
fere
nce
sch
eme
around t
he
velo
city
loca
tion
¶vi
¶t
»Hv iL i,j,
kn
+1-Hv iL i,j,
kn
Dt
¶p
¶x1
»pi,j,k
n-pi
-1,j,k
n
Dx1
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Nu
meri
cal
Dis
creti
zati
on
s(C
on
td.)
•th
e co
nve
ctio
n t
erm
s ar
e dis
cret
ized
usi
ng a
skew
-sym
met
ric
appro
ach t
hat
req
uir
es t
he
calc
ula
tion o
f in
terp
ola
ted
val
ues
fo
r th
e ve
loci
ty c
om
ponen
ts a
t th
e st
agg
ered
loca
tions.
This
le
ads
to t
he
follo
win
g c
ases
for
such
dis
cret
izat
ions:
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Pro
ble
m C
om
pon
en
ts
•The
rele
ase
of
the
pollu
tant
can b
e m
odel
ed
as t
ransv
erse
inje
ctio
n o
f je
ts in c
ross
flo
w (
JIC
F)
•A
JIC
F si
mula
tion w
ithout
the
elev
ated
sourc
e w
as
use
d t
o a
nal
yze
the
salie
nt
flow
fea
ture
s an
d t
hei
r re
spec
tive
dyn
amic
s•The
flow
of
the
pollu
tant
and c
arri
er f
luid
pas
t th
e co
mple
x b
uild
ings
is
model
ed a
s fl
ow
pas
t blu
ff
bodie
s
•A
model
of
flow
pas
t co
mple
x o
bst
acle
s ar
ranged
in
the
form
of
“CC
T”
was
st
udie
d
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Flo
w p
ast
CC
T s
tream
lin
es
•The
pro
ble
m o
f fl
ow
pas
t obst
acle
s sh
ow
s th
e re
circ
ula
tion r
egio
ns
as w
ell as
th
e per
iodic
vort
ex s
hed
din
g t
hat
occ
urs
in t
he
wak
e of
the
last
obst
acle
(th
e le
tter
T in t
he
case
of
the
blu
ff b
odie
s ar
ranged
in t
he
form
of
“CC
T”)
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Jets
In
Cro
ss F
low
V
ect
ors
& C
url
of
Velo
city
fie
ld
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Poll
uta
nt
Dis
pers
ion
V
ect
ors
& C
url
of
velo
city
fie
ld
•The
reci
rcula
tion r
egio
ns
that
appea
r bet
wee
n
the
build
ings
and in
the
wak
e of
the
build
ings
are
more
com
ple
x b
ecau
se o
f th
e in
fluen
ce o
f dif
fere
nt
build
ings
but
still
dis
pla
y th
e gen
eral
pat
tern
s as
soci
ated
wit
h w
akes
.
•Si
nce
this
pre
limin
ary
sim
ula
tion w
as r
un a
t a
low
Rey
nold
s num
ber
(~100)
wit
h c
oar
se m
esh
reso
luti
on, it
does
not
addre
ss t
urb
ule
nt
flow
phen
om
ena
and d
etai
led f
low
phys
ics.
S1
S2
T2
T1
P
S1
T1
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Poll
uta
nt
con
cen
trati
on
evolu
tion
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
t 0t 1
t 2
t 3t 4
t 5
Poll
uta
nt
con
cen
trati
on
evolu
tion
(C
otn
d.)
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
t� 0t� 1
t� 2
t� 3t� 4
t� 5
Con
clu
sio
ns
•T
he
com
bin
atio
n o
f JIC
F an
d f
low
pas
t b
uild
ing
s pro
duce
s a
much
more
com
ple
x f
low
fie
ld.
•T
he
hig
h c
once
ntr
atio
n (
10
%)
is c
onta
ined
wit
hin
the
spac
e bet
wee
n t
he
two t
alle
r b
uild
ings;
this
reg
ion is
also
the
loca
tion o
f th
e hig
hes
t fl
ow
vel
oci
ty.
•T
he
low
conce
ntr
atio
n (
1%
) se
ems
to b
e dif
fuse
d o
ver
a ve
ry
larg
e ar
ea a
round t
he
exit
pla
ne
of
the
com
puta
tional
dom
ain.
It a
lso d
ispla
ys s
om
e per
iodic
var
iati
ons
(i.e
. fl
appin
g)
in t
he
conce
ntr
atio
n iso
surf
ace
that
exte
nds
beh
ind t
he
talle
r build
ing
(T
1).
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Fu
ture
dir
ect
ion
s
•D
iver
sify
the
applic
atio
ns
of
the
CFD
Toolk
it b
ased
on t
he
inte
rest
s of
the
CFD
com
munit
y an
d f
urt
her
dev
elop t
hes
e to
ols
in t
he
req
uir
ed d
irec
tions.
•Pa
ralle
lizin
g t
he
code
for
the
boundar
y co
ndit
ions
to a
llow
fo
r si
mula
tions
wit
h b
luff
bodie
s (i.e
. build
ings)
to r
un o
n t
he
super
com
pute
rs lik
e Su
per
Mik
eat
LSU
.
•A
pply
ing
the
pollu
tant
dis
per
sion p
roble
m t
o a
rea
l ci
tysc
ape
(will
nee
d t
he
par
alle
lizat
ion o
f ob
stac
les
BCs)
•C
hec
kout
the
Cac
tus
CFD
Toolk
it w
ebpag
e fo
r m
ore
in
form
atio
n: http://www.cactuscode.org/Community/CFDToolkit/
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Ack
now
led
gem
en
ts
•T
he
Cen
ter
for
Com
puta
tion &
Tec
hnolo
gy
at L
SU f
or
thei
r ex
celle
nt
tech
nic
al,
acad
emic
and o
rgan
izat
ional
supp
ort
.
•I w
ould
lik
e to
than
k D
r.G
abri
elle
Alle
n,
Mr.
Yaa
koub
el
Kham
ra a
nd
Dr.
May
ank
Tya
gi fo
r th
eir
hel
p d
uri
ng t
his
re
sear
ch.
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
Qu
esti
on
s?
Stud
y of
Polluta
nt D
ispe
rsion
in U
rban
Env
iron
men
t
Carb
unes
cu R
azva
n Co
rnel
iu
