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e
p
r
ed
ictio
n
o
f
t
h
e
co
o
lan
t
ca
p
ab
ilit
y
b
ec
o
m
e
s
m
u
ch
m
o
r
e
elu
s
i
v
e.
T
h
er
ef
o
r
e,
d
esig
n
i
n
g
f
u
ll
n
u
m
er
ic
al
m
o
d
els
th
at
ca
n
s
i
m
u
ltan
eo
u
s
l
y
co
n
s
id
er
cu
r
v
at
u
r
e,
p
o
r
o
u
s
r
esis
ta
n
ce
a
n
d
m
ag
n
et
ic
e
f
f
ec
t
s
h
as
g
ain
ed
m
o
r
e
i
m
p
o
r
tan
ce
i
n
th
e
d
esig
n
,
a
n
d
th
e
o
p
ti
m
izatio
n
o
f
co
o
lin
g
s
y
s
te
m
s
f
o
r
f
u
s
io
n
r
ea
cto
r
s
.
Deta
iled
p
ar
ts
o
f
th
ese
tr
a
n
s
p
o
r
t
p
r
o
ce
s
s
es
h
av
e
b
ee
n
th
e
s
u
b
j
ec
t
o
f
in
ten
s
e
in
v
e
s
ti
g
at
io
n
s
.
E
ar
l
y
s
tu
d
ie
s
led
to
th
e
p
r
ed
ictio
n
o
f
b
asic
s
tate
p
atter
n
s
o
f
s
u
c
h
f
l
u
id
s
an
d
co
n
f
ir
m
ed
th
e
i
m
p
o
r
tan
ce
o
f
L
o
r
en
tz
f
o
r
ce
s
f
o
r
m
o
m
e
n
t
u
m
tr
a
n
s
p
o
r
tatio
n
an
d
f
lo
w
s
tab
ilizatio
n
[
4
]
,
[
5
]
.
C
lass
ical
r
es
u
lts
o
n
cu
r
v
ed
-
c
h
a
n
n
e
l
h
y
d
r
o
d
y
n
a
m
ic
s
also
p
r
o
v
e
th
at
cu
r
v
at
u
r
e
in
d
u
ce
s
s
ec
o
n
d
ar
y
f
lo
w
a
n
d
alter
s
th
e
v
e
lo
cit
y
p
r
o
f
ile
v
ia
t
h
e
ac
tio
n
o
f
ce
n
tr
if
u
g
al
f
o
r
ce
s
,
i
m
p
ac
tin
g
t
h
e
d
is
tr
ib
u
tio
n
o
f
p
r
es
s
u
r
e
a
n
d
co
n
s
eq
u
en
tl
y
,
th
e
to
tal
e
n
er
g
y
o
f
th
e
f
lo
w
[
6
]
,
[
7
]
.
Me
an
w
h
ile,
tr
a
n
s
p
o
r
t
in
p
o
r
o
u
s
m
ed
ia
h
as
b
ee
n
ex
ten
s
i
v
el
y
s
tu
d
ied
u
n
d
er
Dar
c
y
,
B
r
in
k
m
a
n
a
n
d
Fo
r
ch
h
ei
m
er
(
f
o
r
b
o
th
v
i
s
co
u
s
d
if
f
u
s
io
n
a
n
d
in
er
tial
r
esi
s
ta
n
ce
)
ter
m
s
f
o
r
v
ar
io
u
s
t
y
p
es
o
f
p
er
m
ea
b
le
m
ed
ia
[
8
]
–
[
1
2
]
.
Fu
r
th
er
r
esear
ch
h
a
s
g
en
er
alize
d
th
e
s
e
id
ea
s
to
MH
D
h
ea
t
-
tr
an
s
f
er
p
r
o
b
le
m
s
an
d
h
as
u
n
d
er
s
co
r
ed
th
e
n
ee
d
to
co
n
s
id
er
th
er
m
al
tr
an
s
p
o
r
t,
p
r
ess
u
r
e
lo
s
s
es,
an
d
m
ag
n
etic
d
a
m
p
e
n
i
n
g
co
n
cu
r
r
en
tl
y
in
h
ig
h
-
te
m
p
er
atu
r
e
liq
u
id
-
m
etal
co
o
lan
ts
s
y
s
te
m
s
[
1
3
]
–
[
2
0
]
.
W
h
ile
th
ese
r
esear
ch
w
o
r
k
s
p
r
o
v
id
ed
s
u
b
s
tan
tia
l
co
n
tr
ib
u
tio
n
s
in
MH
D
f
lo
w
s
,
cu
r
v
ed
-
c
h
a
n
n
e
l
tr
an
s
p
o
r
t
an
d
p
o
r
o
u
s
-
m
ed
i
u
m
m
o
d
elli
n
g
,
th
e
m
aj
o
r
it
y
o
f
th
e
p
r
ev
io
u
s
l
y
r
ep
o
r
ted
s
tu
d
ies
o
n
th
ese
p
h
y
s
ica
l
m
ec
h
a
n
i
s
m
s
h
av
e
b
ee
n
co
n
d
u
cted
eith
er
s
ep
ar
atel
y
o
r
o
n
a
f
e
w
,
ele
m
en
tar
y
co
u
p
led
v
er
s
i
o
n
s
o
f
t
h
e
m
.
T
h
u
s
,
th
e
ef
f
ec
t
o
f
ch
a
n
n
el
cu
r
v
atu
r
e,
p
o
r
o
u
s
r
esis
ta
n
ce
,
m
ag
n
eti
c
d
am
p
i
n
g
,
p
r
ess
u
r
e
ev
o
lu
t
io
n
,
an
d
h
ea
t
tr
an
s
f
e
r
h
as
y
et
to
b
e
th
o
r
o
u
g
h
l
y
i
n
v
e
s
tig
a
ted
in
a
s
in
g
le
n
u
m
er
ical
s
ch
e
m
e
in
a
m
an
n
er
to
ex
a
m
i
n
e
th
e
p
er
f
o
r
m
an
ce
o
f
v
ar
io
u
s
f
u
s
io
n
-
r
elev
a
n
t c
o
o
lan
ts
at
t
h
e
s
a
m
e
o
p
er
atin
g
co
n
d
itio
n
s
[
2
1
]
,
[
2
2
]
.
T
o
o
v
er
co
m
e
t
h
ese
is
s
u
e
s
,
i
n
t
h
is
w
o
r
k
,
a
co
u
p
led
fi
n
i
t
e
-
d
iffer
en
ce
s
i
m
u
latio
n
m
et
h
o
d
o
lo
g
y
i
s
estab
lis
h
ed
to
in
v
esti
g
ate
M
H
D
fl
o
w
a
n
d
h
ea
t tr
an
s
f
er
i
n
a
t
w
o
-
d
i
m
e
n
s
io
n
al
c
u
r
v
ed
p
o
r
o
u
s
co
o
lin
g
c
h
a
n
n
e
l o
f
th
e
f
u
s
io
n
r
ea
cto
r
b
lan
k
et
s
y
s
t
e
m
.
R
a
th
er
t
h
a
n
is
o
lated
p
h
y
s
ical
m
ec
h
a
n
is
m
s
,
a
s
i
n
ea
r
lier
p
ap
er
s
,
th
e
m
o
d
el
co
n
s
id
er
s
ch
a
n
n
el
c
u
r
v
at
u
r
e
,
B
r
in
k
m
a
n
v
i
s
co
u
s
d
iff
u
s
i
o
n
,
Dar
cy
p
er
m
ea
b
ilit
y
,
Fo
r
ch
h
ei
m
er
in
er
tial
r
esis
ta
n
ce
,
L
o
r
en
tz
-
f
o
r
ce
d
a
m
p
in
g
,
p
r
es
s
u
r
e
e
v
o
lu
tio
n
,
a
n
d
co
n
v
ec
t
iv
e
h
ea
t
tr
an
s
f
er
all
at
o
n
ce
i
n
a
s
i
n
g
le
co
m
p
u
tatio
n
al
f
o
r
m
u
la
tio
n
.
T
h
e
n
u
m
er
ical
r
ea
lizatio
n
i
s
d
o
n
e
in
M
A
T
L
A
B
,
allo
w
i
n
g
f
o
r
th
e
co
m
p
u
ta
tio
n
al
ef
fi
cie
n
c
y
n
ee
d
ed
to
m
ai
n
tai
n
n
u
m
er
ical
s
tab
ilit
y
w
h
ile
s
y
s
te
m
a
ticall
y
s
t
u
d
y
in
g
t
h
e
co
u
p
led
tr
an
s
p
o
r
t
p
r
o
ce
s
s
es
u
n
d
er
t
h
e
s
a
m
e
o
p
er
atin
g
co
n
d
itio
n
s
.
I
n
a
d
d
itio
n
,
th
e
f
r
a
m
e
w
o
r
k
t
h
at
is
i
n
tr
o
d
u
ce
d
h
er
e
is
u
s
ed
to
p
r
ed
ict
an
d
co
m
p
ar
e
th
e
t
h
e
r
m
o
-
h
y
d
r
au
lics
p
er
f
o
r
m
a
n
ce
o
f
a
n
u
m
b
er
o
f
p
o
ten
t
ial
c
o
o
lan
ts
f
o
r
f
u
s
io
n
ap
p
licatio
n
s
s
u
ch
w
ater
,
h
eli
u
m
,
P
b
-
1
7
L
i
,
an
d
P
b
-
1
7
L
i e
n
h
a
n
ce
d
w
i
th
A
l
N
n
a
n
o
p
ar
ticles [
2
3
]
,
[
2
4
]
.
Hen
ce
,
th
e
m
ai
n
n
o
v
elt
y
b
r
o
u
g
h
t
b
y
th
is
w
o
r
k
r
esid
es
in
th
e
f
ac
t
th
at
an
o
v
er
ar
ch
in
g
n
u
m
er
ical
m
o
d
el
h
as
b
ee
n
i
n
tr
o
d
u
ce
d
allo
w
i
n
g
a
n
u
m
b
er
o
f
p
h
y
s
ica
l
ef
f
ec
ts
,
u
s
u
a
ll
y
tr
ea
ted
s
ep
a
r
atel
y
in
t
h
e
m
o
s
t
r
ec
en
t liter
at
u
r
e,
to
b
e
co
m
b
i
n
ed
in
o
n
e
s
i
n
g
le
s
i
m
u
lat
io
n
to
o
l.
T
h
is
h
o
lis
tic
f
o
r
m
u
latio
n
al
lo
w
s
th
e
co
n
cu
r
r
en
t
p
r
ed
ictio
n
o
f
v
elo
cit
y
,
p
r
ess
u
r
e,
an
d
tem
p
er
at
u
r
e
d
is
tr
ib
u
tio
n
s
an
d
also
p
r
o
v
id
es
a
co
m
m
o
n
u
n
d
er
p
in
n
i
n
g
f
o
r
th
e
a
s
s
es
s
m
en
t
o
f
co
o
lan
t
p
er
f
o
r
m
a
n
ce
i
n
a
n
ac
t
u
al
f
u
s
io
n
r
ea
cto
r
en
v
ir
o
n
m
e
n
t.
T
h
e
n
o
v
el
u
n
i
f
ied
s
o
l
u
tio
n
f
ac
ilit
ate
s
a
b
etter
i
n
s
i
g
h
t
o
f
th
e
co
m
p
lica
ted
p
h
en
o
m
en
o
n
o
f
m
a
g
n
e
tic
d
a
m
p
i
n
g
co
m
p
etin
g
w
it
h
p
o
r
o
u
s
r
esis
ta
n
ce
in
a
cu
r
v
ed
ch
a
n
n
el,
an
d
h
en
ce
,
en
ab
le
s
b
etter
co
o
lan
t
p
r
ep
ar
atio
n
an
d
ch
an
n
el
d
esi
g
n
i
n
m
o
r
e
ad
v
an
ce
d
f
u
s
io
n
en
er
g
y
s
y
s
te
m
s
[
2
5
]
.
I
n
ad
d
itio
n
to
its
n
u
m
er
ical
v
a
lu
e,
th
e
ap
p
licab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
c
o
m
p
u
tatio
n
al
f
r
a
m
e
wo
r
k
is
w
it
h
r
ec
o
n
f
i
g
u
r
ab
le
an
d
e
m
b
ed
d
ed
s
y
s
te
m
s
.
T
h
e
f
i
n
ite
-
d
if
f
er
en
ce
s
ch
e
m
e
d
ev
elo
p
ed
in
th
i
s
w
o
r
k
is
a
co
m
p
u
tatio
n
al
k
er
n
e
l
th
at
ca
n
b
e
p
o
r
ted
to
em
b
ed
d
ed
m
o
n
i
to
r
in
g
p
latf
o
r
m
s
,
d
ig
ital
t
w
i
n
en
v
ir
o
n
m
e
n
t
s
,
an
d
r
ea
l
-
ti
m
e
t
h
er
m
al
m
a
n
ag
e
m
e
n
t
s
o
l
u
tio
n
s
f
o
r
f
u
s
io
n
r
ea
ct
o
r
s
.
W
ith
f
as
t
p
r
ed
ictio
n
o
f
th
er
m
o
-
h
y
d
r
au
l
ic
p
er
f
o
r
m
a
n
ce
b
ased
o
n
th
e
tes
ted
o
p
er
atin
g
co
n
d
itio
n
,
th
e
a
p
p
r
o
ac
h
ca
n
en
ab
le
in
telli
g
en
t
m
o
n
ito
r
i
n
g
,
f
au
l
t
di
ag
n
o
s
i
s
,
an
d
p
r
ed
ictiv
e
co
n
tr
o
l
s
tr
ateg
ies
w
i
th
i
n
ter
n
et
o
f
th
in
g
(
I
o
T
)
-
en
ab
led
s
en
s
i
n
g
in
f
r
a
s
tr
u
ct
u
r
es.
I
n
ad
d
itio
n
,
th
e
al
g
o
r
ith
m
i
s
al
s
o
h
ar
d
w
ar
e
-
f
r
ien
d
l
y
,
allo
w
i
n
g
f
o
r
th
e
p
o
s
s
ib
ilit
y
o
f
b
ein
g
m
a
p
p
ed
o
n
h
ar
d
w
ar
e
ac
ce
ler
ato
r
s
s
u
c
h
as
f
ield
-
p
r
o
g
r
a
m
m
ab
le
g
ate
ar
r
a
y
(
FP
G
A
)
an
d
v
er
y
-
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A
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Evaluation Warning : The document was created with Spire.PDF for Python.
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2.
P
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CA
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M
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L
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Q
UAT
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O
N
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2
.
1
.
G
eo
m
et
ry
a
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co
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rdina
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y
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t
e
m
T
h
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ain
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f
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,
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.
T
h
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co
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in
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w
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(
=
0
)
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d
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in
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ter
w
all
(
)
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T
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li
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lo
w
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T
h
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R
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tu
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s
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f
cu
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ch
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lo
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s
[
6
]
,
[
7
]
.
On
th
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b
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th
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ap
p
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[
8
]
,
[
9
]
.
T
h
e
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s
e
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f
a
p
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lar
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ate
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at
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C
ar
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in
ates.
T
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ch
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n
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b
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n
d
ar
y
as
→
∞
[
1
6
]
–
[
1
8
]
.
Fig
u
r
e
1
illu
s
tr
ates
t
h
e
p
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y
s
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f
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Fig
u
r
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1
(
a)
s
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F
ig
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(
a)
(
b
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Fig
u
r
e
1
.
Sch
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m
atic
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co
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(
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)
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atic
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tr
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2
.
2
.
M
o
delin
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a
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s
u
m
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s
a
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ph
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s
ica
l f
ra
m
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Fo
r
m
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la
s
f
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th
e
s
y
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m
o
f
eq
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t
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f
lo
w
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f
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i
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co
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p
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ess
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t
at
l
o
w
M
ac
h
n
u
m
b
er
s
r
elev
a
n
t
to
f
u
s
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r
ea
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co
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lin
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s
.
Fl
u
id
d
en
s
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y
(
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an
d
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ity
(
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w
e
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ted
as
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s
ta
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,
an
d
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m
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to
o
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tain
a
d
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g
en
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-
f
r
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v
elo
cit
y
f
ield
[
1
6
]
–
[1
8
]
.
T
h
e
p
o
r
o
u
s
m
ed
i
u
m
w
as
r
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r
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ted
u
s
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Dar
c
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B
r
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a
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Fo
r
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lati
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w
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t
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r
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al
l
w
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th
i
n
t
h
e
p
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u
s
m
atr
i
x
[
8
]
–
[1
2
]
.
I
t
w
as a
l
s
o
ass
u
m
ed
th
at
t
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p
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T
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D
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R
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ield
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h
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L
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h
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J
o
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ai
n
tai
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en
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g
y
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n
s
i
s
te
n
c
y
[
1
3
]
–
[
1
5
]
.
T
h
e
m
at
h
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m
atica
l
m
o
d
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is
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D
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M
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B
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h
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ical
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ties
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tili
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d
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i
m
u
l
atio
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ar
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r
esen
ted
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4864
S
o
ftw
a
r
e
s
imu
la
tio
n
o
f m
a
g
n
et
o
h
yd
r
o
d
y
n
a
mic
co
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flo
w
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ve
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…
(
Ha
s
s
a
n
Mo
h
a
mm
a
d
Ha
s
s
a
n
)
659
2
.
3
.
Dim
e
ns
io
na
l g
o
v
er
nin
g
equa
t
io
ns
Fo
r
th
e
p
h
y
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ical
m
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el
a
n
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ass
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m
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tio
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le
f
lo
w
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n
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ea
t
tr
an
s
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er
i
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a
cu
r
v
ed
p
o
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u
s
ch
a
n
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l
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d
er
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ed
as
f
o
llo
w
s
in
th
e
(
,
)
co
o
r
d
in
ate
s
y
s
te
m
[
1
6
]
–
[
1
8
]
:
f
lo
w
:
(
)
an
d
(
)
;
;
;
in
co
r
p
o
r
atin
g
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ec
ts
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r
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a
tu
r
e
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e
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ca
l
r
ad
iu
s
(
+
)
,
as
d
ef
in
ed
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n
s
u
b
s
ec
ti
o
n
2
.
1
.
Un
d
er
th
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in
co
m
p
r
e
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s
ib
ilit
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a
s
s
u
m
p
tio
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o
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ted
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th
is
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t
u
d
y
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e
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n
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it
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eq
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atio
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ed
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ce
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to
:
1
+
(
(
+
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+
+
(
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=
0
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1
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T
h
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ad
ial
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d
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g
en
t
ial
m
o
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en
tu
m
eq
u
a
tio
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s
ar
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ex
p
r
ess
ed
as
(
2
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an
d
(
3
)
:
(
+
+
(
+
)
−
2
+
)
=
−
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[
2
2
+
(
1
+
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(
2
(
+
)
2
)
2
2
−
(
+
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2
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−
−
|
|
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[
(
·
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(
2
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an
d
(
+
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−
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[
(
·
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(
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A
cc
o
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n
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o
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tr
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.
R
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ce
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ed
b
y
t
h
e
p
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s
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ed
iu
m
th
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h
Dar
c
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d
Fo
r
ch
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e
i
m
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d
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m
s
w
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n
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r
-
w
all
s
h
ea
r
is
r
etain
ed
v
ia
B
r
in
k
m
a
n
co
n
tr
ib
u
tio
n
.
T
h
e
g
o
v
e
r
n
in
g
eq
u
a
tio
n
s
ac
co
u
n
t
f
o
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tr
an
s
ie
n
t,
co
n
v
ec
t
iv
e,
a
n
d
v
is
co
u
s
e
f
f
ec
ts
.
P
o
r
o
u
s
r
esi
s
tan
ce
is
in
tr
o
d
u
ce
d
th
r
o
u
g
h
t
h
e
Dar
c
y
a
n
d
Fo
r
ch
h
ei
m
er
d
r
ag
ter
m
s
,
w
h
ile
n
e
ar
-
w
all
s
h
ea
r
is
r
etai
n
ed
th
r
o
u
g
h
t
h
e
B
r
in
k
m
a
n
co
n
tr
ib
u
tio
n
[
8
]
–
[
1
2
]
.
MH
D
in
ter
ac
tio
n
s
ar
e
r
ep
r
ese
n
ted
th
r
o
u
g
h
t
h
e
L
o
r
en
tz
-
f
o
r
ce
ter
m
[
1
3
]
–
[
1
5
]
.
C
u
r
v
atu
r
e
-
i
n
d
u
ce
d
in
er
t
ial
ef
f
ec
ts
ar
e
in
tr
o
d
u
ce
d
th
r
o
u
g
h
t
h
e
lo
ca
l r
ad
iu
s
(
+
)
[
6
]
,
[
7
]
.
T
h
e
p
r
ess
u
r
e
f
ield
is
n
o
t p
r
escr
ib
ed
ex
p
licitl
y
b
u
t i
s
o
b
tain
ed
n
u
m
er
icall
y
f
r
o
m
its
s
p
atial
g
r
ad
ien
ts
:
=
−
[
+
+
(
+
)
−
2
+
]
+
[
2
2
+
(
1
+
)
+
(
2
(
+
)
2
)
2
2
−
(
+
)
2
]
−
−
|
|
+
+
[
(
·
)
−
2
]
(
4
)
an
d
+
=
−
[
+
+
(
+
)
+
+
]
+
[
²
²
+
(
1
+
)
+
(
²
(
+
)
2
)
²
²
−
(
+
)
2
]
−
−
|
|
+
+
[
(
·
)
−
²
]
(
5
)
e
n
s
u
r
in
g
co
n
s
is
te
n
c
y
w
it
h
m
a
s
s
co
n
s
er
v
a
t
io
n
a
n
d
m
o
m
e
n
t
u
m
b
alan
ce
[
1
6
]
–
[
1
9
]
.
T
h
e
en
er
g
y
eq
u
at
io
n
g
o
v
er
n
i
n
g
h
ea
t tr
a
n
s
f
er
in
t
h
e
co
o
lan
t i
s
w
r
i
tten
a
s
(
6
)
:
[
(
1
−
)
,
+
,
]
+
,
(
+
+
)
−
(
+
+
+
)
=
(
2
2
+
1
+
+
2
(
+
)
2
2
2
)
+
+
2
(
+
)
2
+
+
+
Φ
(
6
)
w
h
er
e
h
ea
t
tr
an
s
p
o
r
t
b
y
co
n
v
ec
tio
n
a
n
d
co
n
d
u
ctio
n
i
s
co
n
s
id
er
ed
.
Vo
lu
m
etr
ic
h
ea
t
g
e
n
er
atio
n
an
d
v
is
co
u
s
d
is
s
ip
atio
n
ar
e
i
n
cl
u
d
ed
w
h
er
e
ap
p
licab
le,
an
d
J
o
u
le
h
ea
tin
g
is
k
ep
t
f
o
r
elec
tr
icall
y
co
n
d
u
cti
v
e
f
lu
id
s
u
n
d
er
MH
D
co
n
d
itio
n
s
[
1
3
]
,
[
1
4
]
,
[
2
0
]
.
In
(
1
)
–
(
6
)
co
n
s
titu
te
a
co
u
p
led
s
y
s
te
m
d
escr
ib
in
g
th
e
tr
an
s
p
o
r
t
o
f
m
a
s
s
,
m
o
m
en
t
u
m
,
p
r
ess
u
r
e
g
r
ad
ien
ts
,
a
n
d
en
er
g
y
i
n
a
cu
r
v
ed
p
o
r
o
u
s
ch
an
n
el
s
u
b
j
ec
ted
to
h
y
d
r
o
m
ag
n
etic
e
f
f
ec
ts
.
T
h
e
s
y
s
te
m
i
s
s
o
lv
ed
n
u
m
er
icall
y
s
u
b
j
ec
t to
th
e
b
o
u
n
d
ar
y
co
n
d
itio
n
s
s
p
ec
i
f
ied
in
s
u
b
s
ec
tio
n
2
.
4.
2
.
4
.
B
o
un
da
ry
co
nd
it
io
ns
T
h
e
g
o
v
er
n
i
n
g
eq
u
at
io
n
s
ar
e
s
o
lv
ed
i
n
t
h
e
(
,
)
d
o
m
ain
s
u
b
j
ec
t
to
th
e
f
o
llo
w
i
n
g
d
i
m
e
n
s
i
o
n
al
b
o
u
n
d
ar
y
co
n
d
itio
n
s
.
T
h
e
s
tr
e
a
m
w
i
s
e
co
o
r
d
in
ate
is
ali
g
n
ed
th
e
m
ai
n
f
lo
w
d
ir
ec
tio
n
,
w
it
h
(
=
0
)
d
en
o
ti
n
g
th
e
in
let
an
d
=
at
th
e
o
u
tlet,
w
h
ile
is
th
e
tr
an
s
v
er
s
e
co
o
r
d
in
ate
ac
r
o
s
s
th
e
ch
an
n
e
l
th
ic
k
n
ess
,
w
i
t
h
=
0
at
th
e
in
n
er
w
all
a
n
d
=
at
th
e
o
u
ter
w
all.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4864
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
,
Vo
l.
15
,
No
.
3
,
No
v
e
m
b
er
202
6
:
656
-
670
660
I
n
let
(
=
0
)
A
t t
h
e
i
n
let,
d
ir
ich
let
b
o
u
n
d
ar
y
co
n
d
itio
n
s
ar
e
p
r
escr
ib
ed
f
o
r
th
e
v
elo
cit
y
co
m
p
o
n
e
n
t
s
an
d
t
e
m
p
er
atu
r
e
f
ield
:
(
,
0
)
=
0
,
(
)
=
(
,
0
)
=
(
,
0
)
Her
e,
,
(
)
d
en
o
tes
a
p
r
escr
ib
ed
in
let
v
elo
cit
y
p
r
o
f
ile
ch
o
s
en
to
p
r
o
v
id
e
a
w
ell
-
d
ef
i
n
ed
r
ef
er
en
ce
s
tate
f
o
r
th
e
s
u
b
s
eq
u
e
n
t
f
lo
w
d
e
v
elo
p
m
en
t
[
1
7
]
.
T
h
e
f
lo
w
i
s
d
r
iv
en
b
y
a
co
n
s
tan
t
s
tr
ea
m
w
is
e
p
r
ess
u
r
e
g
r
ad
ien
t
:
=
(
)
W
h
ich
co
r
r
esp
o
n
d
s
to
a
li
n
ea
r
p
r
ess
u
r
e
v
ar
iatio
n
alo
n
g
t
h
e
ch
an
n
el
[
1
9
]
.
T
o
r
em
o
v
e
t
h
e
ar
b
itra
r
y
ad
d
iti
v
e
co
n
s
ta
n
t in
t
h
e
p
r
ess
u
r
e
f
ield
,
a
p
r
ess
u
r
e
r
ef
er
en
ce
i
s
f
i
x
ed
at
th
e
o
u
tlet
:
(
,
)
=
Ou
tlet
(
=
)
A
t t
h
e
o
u
tle
t,
ze
r
o
-
g
r
ad
ien
t (
o
u
t
f
lo
w
)
co
n
d
itio
n
s
ar
e
ap
p
lied
to
th
e
tr
an
s
p
o
r
ted
v
ar
iab
les:
|
=
=
0
,
|
=
=
0
,
|
=
=
0
A
llo
w
i
n
g
a
s
m
o
o
t
h
ex
it o
f
t
h
e
f
lo
w
an
d
t
h
er
m
al
f
ield
s
w
i
th
o
u
t i
m
p
o
s
in
g
ar
ti
f
icial
co
n
s
tr
ai
n
ts
.
So
lid
w
all
s
, n
o
-
s
lip
co
n
d
itio
n
s
ar
e
en
f
o
r
ce
d
at
b
o
th
ch
an
n
el
w
all
s
:
(
0
,
)
=
(
0
,
)
=
0
,
(
,
)
=
(
,
)
=
0
T
h
er
m
al
b
o
u
n
d
ar
y
co
n
d
itio
n
s
:
t
h
er
m
al
co
n
d
itio
n
s
at
t
h
e
w
all
s
ar
e
p
r
escr
ib
ed
as:
|
=
0
=
0
,
(
)
(
,
)
=
,
(
ℎ
)
T
h
ese
b
o
u
n
d
ar
y
co
n
d
itio
n
s
u
n
iq
u
el
y
s
p
ec
if
y
th
e
v
elo
cit
y
,
p
r
ess
u
r
e
-
g
r
ad
ien
t
-
d
r
i
v
en
f
lo
w
,
an
d
te
m
p
er
atu
r
e
f
ield
s
,
a
n
d
e
n
s
u
r
e
a
w
ell
-
p
o
s
ed
th
er
m
o
h
y
d
r
o
d
y
n
a
m
ic
p
r
o
b
lem
f
o
r
t
h
e
c
u
r
v
ed
p
o
r
o
u
s
ch
an
n
e
l
u
n
d
er
h
y
d
r
o
m
a
g
n
etic
co
n
d
itio
n
s
.
2
.
5
.
No
n
-
di
m
ens
io
na
l f
o
r
m
u
la
t
io
n a
nd
g
o
v
er
nin
g
pa
ra
m
et
er
s
T
o
r
ed
u
ce
th
e
g
o
v
er
n
in
g
eq
u
a
tio
n
s
to
a
d
i
m
e
n
s
io
n
les
s
f
o
r
m
an
d
to
id
en
tify
t
h
e
co
n
tr
o
lli
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h
y
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ical
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ec
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a
n
i
s
m
s
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e
f
o
llo
w
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g
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ef
er
en
ce
s
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le
s
ar
e
in
tr
o
d
u
ce
d
:
th
e
tr
an
s
v
er
s
e
len
g
t
h
s
ca
le
,
th
e
s
tr
ea
m
w
is
e
len
g
th
s
ca
le
,
a
ch
ar
ac
ter
is
tic
v
elo
cit
y
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e
ti
m
e
s
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le
0
=
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e
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r
ess
u
r
e
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ca
le
=
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2
,
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d
th
e
te
m
p
er
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r
e
s
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le
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h
e
d
im
e
n
s
io
n
le
s
s
v
ar
iab
le
s
ar
e
d
ef
in
ed
as
:
=
∗
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=
∗
,
=
0
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,
=
0
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=
∗
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⁄
,
=
0
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=
0
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=
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|
|
=
0
|
∗
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,
=
0
∗
,
Θ
=
−
∆
,
=
0
∗
T
h
e
g
eo
m
etr
ic
cu
r
v
at
u
r
e
en
te
r
s
th
e
f
o
r
m
u
latio
n
th
r
o
u
g
h
th
e
lo
ca
l
r
ad
iu
s
(
+
)
.
I
n
d
im
e
n
s
io
n
l
es
s
f
o
r
m
,
th
is
q
u
a
n
tit
y
ap
p
ea
r
s
as
:
∗
=
+
,
∗
=
+
,
∗
=
+
W
h
ich
i
s
r
etain
ed
ex
p
lici
tl
y
i
n
th
e
g
o
v
er
n
i
n
g
eq
u
atio
n
s
to
ac
co
u
n
t
f
o
r
cu
r
v
at
u
r
e
-
in
d
u
ce
d
ce
n
tr
if
u
g
al
e
f
f
ec
t
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4864
S
o
ftw
a
r
e
s
imu
la
tio
n
o
f m
a
g
n
et
o
h
yd
r
o
d
y
n
a
mic
co
o
lin
g
flo
w
in
cu
r
ve
d
…
(
Ha
s
s
a
n
Mo
h
a
mm
a
d
Ha
s
s
a
n
)
661
C
o
n
ti
n
u
it
y
co
n
s
tr
ain
t
,
u
n
d
er
th
e
in
co
m
p
r
ess
ib
il
it
y
as
s
u
m
p
tio
n
an
d
co
n
s
ta
n
t
p
o
r
o
s
ity
(
)
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th
e
co
n
tin
u
it
y
eq
u
atio
n
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ed
u
ce
s
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a
d
iv
er
g
en
ce
-
f
r
ee
co
n
s
tr
ai
n
t
o
n
th
e
v
elo
cit
y
f
ield
:
1
∗
∗
(
∗
∗
)
+
1
∗
∗
(
∗
)
=
0
(
7
)
T
h
is
r
elatio
n
r
ep
r
esen
ts
co
n
s
er
v
atio
n
o
f
m
as
s
in
th
e
p
o
r
o
u
s
cu
r
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ed
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n
e
l.
Su
b
s
tit
u
ti
n
g
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e
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o
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e
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ca
lin
g
s
in
to
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h
e
d
i
m
en
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io
n
a
l
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r
in
k
m
an
–
Fo
r
c
h
h
ei
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er
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M
HD
m
o
m
en
t
u
m
eq
u
at
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n
s
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t
h
e
n
o
n
-
d
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m
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n
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io
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al
m
o
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e
n
t
u
m
eq
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s
i
n
th
e
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a
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ial
(
r
)
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d
tan
g
en
t
ial
(
s
)
d
ir
ec
tio
n
s
ar
e
w
r
itte
n
as:
a.
R
ad
ial
m
o
m
en
tu
m
eq
u
atio
n
T
h
e
co
n
v
er
g
e
n
ce
o
f
th
e
n
u
m
er
ical
s
o
l
u
tio
n
is
c
h
ec
k
ed
b
y
u
s
in
g
t
h
e
ca
lib
r
ated
r
esid
u
als
o
f
t
h
e
v
elo
cit
y
a
n
d
te
m
p
er
at
u
r
e
f
iel
d
s
.
I
ter
atio
n
s
ar
e
s
to
p
p
ed
w
h
en
th
e
r
e
s
id
u
al
v
al
u
es
o
f
th
e
d
ep
en
d
en
t
v
ar
iab
le
s
w
er
e
w
it
h
i
n
t
h
e
s
p
ec
i
f
ied
to
ler
an
ce
,
an
d
t
h
er
e
w
as
n
o
s
i
g
n
if
i
ca
n
t
c
h
an
g
e
i
n
t
h
e
co
n
to
u
r
l
in
es
o
r
p
r
o
f
iles
o
f
t
h
e
ca
lcu
lated
li
n
es.
T
h
e
u
s
e
o
f
p
ar
tial
atten
u
atio
n
i
m
p
r
o
v
ed
t
h
e
r
o
b
u
s
t
n
e
s
s
o
f
th
e
iter
atio
n
p
r
o
ce
s
s
,
esp
ec
iall
y
i
n
ca
s
es o
f
s
tr
o
n
g
Fo
r
c
h
h
ei
m
er
r
esis
ta
n
ce
o
r
h
ig
h
m
ag
n
etic
i
n
t
er
ac
tio
n
.
A
ze
r
o
-
g
r
ad
ien
t o
u
tp
u
t c
o
n
d
iti
o
n
w
a
s
:
∗
[
∗
∗
+
∗
∗
∗
+
∗
∗
∗
∗
−
∗
2
∗
]
=
−
∗
∗
+
1
[
2
∗
∗
2
+
1
∗
∗
∗
+
2
2
1
∗
2
2
∗
∗
2
−
2
2
∗
∗
2
]
−
1
∗
−
∗
|
∗
|
∗
+
∗
∗
+
[
∗
(
∗
·
∗
)
−
∗
2
∗
]
(
8
)
T
an
g
en
tial
m
o
m
e
n
t
u
m
:
∗
[
∗
∗
+
∗
∗
∗
+
1
∗
∗
∗
∗
−
1
∗
∗
∗
]
=
−
1
∗
∗
∗
+
1
[
2
∗
∗
2
+
1
1
∗
∗
∗
+
1
2
1
∗
2
2
∗
∗
2
−
1
2
∗
∗
2
]
−
1
∗
−
∗
|
∗
|
∗
+
∗
∗
+
[
∗
(
∗
·
∗
)
−
∗
2
∗
]
(
9
)
T
h
es
e
eq
u
atio
n
s
ar
e
p
ar
a
m
ete
r
ized
b
y
v
is
co
u
s
a
n
d
in
er
tia
l
ef
f
ec
ts
t
h
r
o
u
g
h
th
e
B
r
i
n
k
m
a
n
R
e
y
n
o
ld
s
n
u
m
b
er
(
)
,
p
o
r
o
u
s
r
esis
ta
n
ce
th
r
o
u
g
h
t
h
e
co
n
tr
ib
u
tio
n
s
o
f
th
e
Dar
c
y
an
d
Fo
r
ch
h
ei
m
e
r
(
)
,
an
d
h
y
d
r
o
m
a
g
n
etic
e
f
f
ec
t
s
t
h
r
o
u
g
h
th
e
in
ter
ac
tio
n
p
ar
a
m
eter
(
s
tu
ar
t
n
u
m
b
er
)
N.
T
h
e
cu
r
v
a
tu
r
e
ef
f
ec
t
i
s
k
ep
t
ex
p
licitl
y
th
r
o
u
g
h
t
h
e
lo
ca
l r
ad
iu
s
(
∗
)
.
b.
P
r
ess
u
r
e
-
g
r
ad
ien
t r
elatio
n
s
T
h
e
p
r
ess
u
r
e
f
ield
ap
p
ea
r
s
in
th
e
f
o
r
m
u
lat
io
n
th
r
o
u
g
h
its
s
p
atial
g
r
ad
ien
ts
,
w
h
ich
ar
e
o
b
tain
ed
co
n
s
is
ten
tl
y
f
r
o
m
t
h
e
m
o
m
en
t
u
m
b
ala
n
ce
s
.
R
ad
ial
p
r
e
s
s
u
r
e
g
r
ad
ien
t
:
∗
∗
=
−
∗
[
∗
∗
+
∗
∗
∗
+
∗
∗
∗
∗
−
∗
2
∗
]
+
1
[
²
∗
∗
2
+
1
∗
∗
∗
+
2
2
1
∗
2
²
∗
∗
2
−
2
2
∗
∗
2
]
−
1
∗
−
∗
|
∗
|
∗
+
∗
∗
+
[
∗
(
∗
·
∗
)
−
∗
2
∗
]
(1
0
)
T
an
g
en
tial p
r
ess
u
r
e
g
r
ad
ie
n
t
:
1
∗
∗
∗
=
−
∗
[
∗
∗
+
∗
∗
∗
+
1
∗
∗
∗
∗
−
1
∗
∗
∗
]
+
1
[
²
∗
∗
2
+
1
1
∗
∗
∗
+
1
2
1
∗
2
²
∗
∗
2
−
1
2
∗
∗
2
]
−
1
∗
−
∗
|
∗
|
∗
+
∗
∗
+
[
∗
(
∗
·
∗
)
−
∗
2
∗
]
(1
1
)
T
h
ese
r
elatio
n
s
en
s
u
r
e
a
co
n
s
i
s
ten
t c
o
u
p
lin
g
b
et
w
ee
n
p
r
ess
u
r
e
an
d
v
elo
cit
y
i
n
t
h
e
cu
r
v
ed
c
o
o
r
d
in
ate
s
y
s
te
m
.
No
n
-
d
i
m
e
n
s
io
n
al
en
er
g
y
eq
u
a
tio
n
,
t
h
e
d
i
m
en
s
io
n
less
e
n
er
g
y
eq
u
atio
n
g
o
v
er
n
i
n
g
h
ea
t
tr
an
s
f
er
in
t
h
e
p
o
r
o
u
s
cu
r
v
ed
ch
a
n
n
el
i
s
w
r
itt
en
as
(
1
2
)
:
Θ
∗
+
(
∗
Θ
∗
+
1
∗
∗
Θ
∗
)
=
0
(
2
Θ
∗
2
+
1
∗
Θ
∗
+
1
2
1
∗
2
2
Θ
∗
2
)
+
0
∗
∗
Θ
∗
+
0
2
∗
∗
Θ
∗
+
Ω
+
+
Br
2
+
(
∗
∗
+
∗
∗
∗
+
1
∗
∗
∗
∗
)
(1
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4864
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
,
Vo
l.
15
,
No
.
3
,
No
v
e
m
b
er
202
6
:
656
-
670
662
Hea
t
tr
an
s
f
er
b
y
co
n
v
ec
tio
n
a
n
d
d
if
f
u
s
io
n
is
co
n
tr
o
lled
b
y
th
e
P
ec
let
n
u
m
b
er
s
f
o
r
th
e
m
i
x
tu
r
e
a
n
d
th
e
f
l
u
id
(
,
)
.
Vis
co
u
s
d
is
s
ip
atio
n
an
d
J
o
u
le
h
ea
tin
g
ar
e
r
ep
r
esen
ted
b
y
th
e
co
r
r
esp
o
n
d
in
g
E
c
k
e
r
t
(
)
an
d
B
r
in
k
m
a
n
n
u
m
b
er
s
(
)
.
Pre
s
s
u
r
e
-
w
o
r
k
an
d
d
is
s
ip
atio
n
ter
m
s
ar
e
k
ep
t
en
s
u
r
in
g
th
er
m
o
d
y
n
a
m
i
c
co
n
s
is
ten
c
y
u
n
d
er
s
tr
o
n
g
h
y
d
r
o
m
a
g
n
etic
a
n
d
p
o
r
o
u
s
in
f
lu
e
n
ce
s
.
c.
Go
v
er
n
i
n
g
d
i
m
e
n
s
io
n
les
s
p
ar
am
eter
s
In
(
7
)
–
(
1
2
)
c
o
n
s
t
i
tu
te
a
c
l
o
s
ed
,
c
o
u
p
l
e
d
,
n
o
n
-
d
im
en
s
i
o
n
al
s
y
s
tem
d
e
s
c
r
i
b
in
g
m
o
m
en
t
u
m
t
r
a
n
s
p
o
r
t
,
p
r
e
s
s
u
r
e
-
g
r
a
d
i
en
t
-
d
r
iv
en
f
l
o
w
,
a
n
d
h
e
at
t
r
an
s
f
e
r
in
a
cu
r
v
e
d
p
o
r
o
u
s
ch
an
n
el
u
n
d
e
r
h
y
d
r
o
m
ag
n
e
ti
c
c
o
n
d
i
ti
o
n
s
.
T
h
e
d
im
en
s
i
o
n
le
s
s
g
r
o
u
p
s
a
r
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s
i
n
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f
r
o
m
t
h
e
a
b
o
v
e
s
c
a
li
n
g
in
cl
u
d
e
th
e
B
r
in
k
m
an
R
ey
n
o
l
d
s
n
u
m
b
e
r
,
D
a
r
cy
n
u
m
b
e
r
(
)
,
F
o
r
ch
h
e
im
e
r
n
u
m
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e
r
,
F
r
o
u
d
e
n
u
m
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e
r
,
in
te
r
a
c
t
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o
n
p
a
r
am
e
t
e
r
(
S
tu
a
r
t
n
u
m
b
e
r
)
,
m
ix
tu
r
e
a
n
d
f
lu
i
d
Pé
cl
e
t
n
u
m
b
e
r
s
a
n
d
,
E
c
k
e
r
t
n
u
m
b
e
r
,
v
i
s
c
o
u
s
an
d
J
o
u
l
e
B
r
in
k
m
an
n
u
m
b
e
r
s
a
n
d
,
a
n
d
th
e
v
o
lu
m
e
t
r
i
c
h
e
at
g
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e
r
at
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o
n
p
a
r
am
et
e
r
Ω
.
T
h
e
i
r
m
a
th
em
a
t
i
c
a
l
d
ef
in
i
t
i
o
n
s
a
n
d
p
h
y
s
ic
a
l
i
n
te
r
p
r
e
t
a
ti
o
n
s
a
r
e
p
r
o
v
i
d
e
d
in
T
a
b
l
e
S
1
o
f
th
e
s
u
p
p
lem
en
t
a
r
y
m
a
t
e
r
i
a
l
,
f
o
ll
o
w
in
g
t
h
e
s
t
an
d
a
r
d
c
o
n
v
en
t
i
o
n
s
[
1
6
]
–
[
2
1
]
.
2
.
5
.
1
.
P
a
ra
m
et
er
ra
ng
es a
nd
ca
s
e
s
et
up
Du
e
to
th
e
s
ig
n
i
f
ica
n
t
in
ter
d
ep
en
d
en
ce
o
f
ca
m
w
h
ee
l
t
h
er
m
o
p
h
y
s
ical
p
r
o
p
er
ties
in
th
e
w
o
r
k
in
g
f
lu
id
s
co
n
s
id
er
ed
,
id
en
tical
v
al
u
es
o
f
d
i
m
e
n
s
io
n
les
s
p
ar
a
m
eter
s
ar
e
n
o
t
ex
p
ec
ted
to
co
r
r
esp
o
n
d
to
id
en
tical
f
lo
w
o
r
th
er
m
a
l
co
n
d
itio
n
s
.
Hen
ce
f
o
r
ea
ch
co
o
lan
t
w
e
w
i
ll
in
d
ep
en
d
en
tl
y
s
a
m
p
le
t
h
r
ee
r
ep
r
esen
ta
tiv
e
le
v
els
f
o
r
ea
ch
in
f
lu
e
n
tia
l
d
i
m
en
s
io
n
le
s
s
n
u
m
b
er
to
p
r
o
b
e
lo
w
,
in
ter
m
ed
iate
an
d
h
ig
h
r
esp
o
n
s
e
r
eg
i
m
es
i
n
p
h
y
s
icall
y
r
ea
li
s
tic
r
an
g
e
s
.
A
lt
h
o
u
g
h
t
h
e
n
u
m
er
ica
l
v
alu
es
o
f
t
h
e
co
ef
f
icie
n
ts
d
i
f
f
er
f
o
r
ea
ch
f
l
u
id
,
th
e
n
u
m
b
er
o
f
r
esp
o
n
s
e
s
r
e
m
ain
s
co
n
s
tan
t
f
o
r
th
e
s
a
m
e
g
eo
m
etr
y
/b
o
u
n
d
ar
y
co
n
d
itio
n
s
.
T
h
is
allo
w
ed
u
s
to
ass
es
s
th
e
r
elat
iv
e
i
m
p
o
r
tan
ce
o
f
p
r
o
p
er
ties
/co
ef
f
icie
n
ts
in
ab
s
o
lu
te
ter
m
s
,
a
n
d
th
u
s
d
r
a
w
m
ea
n
i
n
g
f
u
l
co
m
p
ar
i
s
o
n
s
b
et
w
ee
n
w
ater
,
h
e
liu
m
,
P
b
-
1
7
L
i a
n
d
P
b
-
1
7
L
i+
A
l
N
n
a
n
o
f
l
u
id
[
2
2
]
–
[
2
4
]
.
3.
RE
S
E
ARCH
M
E
T
H
O
D
R
esear
ch
ap
p
r
o
ac
h
w
as
f
o
r
m
u
lated
o
n
th
e
b
asis
o
f
d
e
v
elo
p
in
g
a
s
o
f
t
w
ar
e
s
i
m
u
latio
n
te
ch
n
iq
u
e
f
o
r
m
o
m
e
n
t
u
m
co
u
p
li
n
g
,
p
r
ess
u
r
e
g
r
ad
ien
t,
a
n
d
h
ea
t
tr
a
n
s
f
er
in
a
b
en
t
p
o
r
o
u
s
r
ea
cto
r
co
o
lin
g
p
ass
a
g
e.
T
h
e
s
o
lu
tio
n
p
r
o
ce
d
u
r
e
f
o
r
n
u
m
er
i
ca
l
s
i
m
u
la
tio
n
co
n
s
i
s
ted
o
f
t
h
e
f
o
llo
w
i
n
g
f
o
u
r
s
tep
s
:
d
eter
m
i
n
atio
n
o
f
c
h
an
n
el
g
eo
m
etr
y
a
n
d
co
o
lan
t
p
r
o
p
er
ties
,
th
e
d
is
cr
etiza
tio
n
o
f
th
e
g
o
v
er
n
i
n
g
eq
u
atio
n
s
o
n
a
2
D
s
tr
u
ct
u
r
ed
g
r
id
,
iter
ativ
e
s
o
lu
t
io
n
o
f
t
h
e
co
u
p
l
ed
v
elo
cit
y
an
d
te
m
p
er
atu
r
e
f
i
eld
s
,
an
d
t
h
e
v
alid
atio
n
o
f
t
h
e
n
u
m
er
ical
s
o
l
u
tio
n
b
y
m
o
n
ito
r
in
g
t
h
e
co
n
v
er
g
e
n
c
e
an
d
co
n
d
u
cti
n
g
g
r
id
-
i
n
d
ep
en
d
en
t
te
s
ts
.
T
h
e
s
i
m
u
latio
n
was
p
er
f
o
r
m
ed
u
s
i
n
g
MA
T
L
A
B
R
2
0
2
5
b
s
o
f
t
w
ar
e.
T
h
e
c
o
m
p
u
tatio
n
al
m
eth
o
d
f
o
r
m
u
lated
i
n
th
i
s
w
o
r
k
ca
n
b
e
d
ir
ec
tl
y
i
m
p
le
m
en
ted
i
n
e
m
b
ed
d
ed
m
o
n
ito
r
in
g
s
y
s
te
m
s
d
u
e
to
its
m
o
d
u
lar
f
i
n
ite
-
d
if
f
er
en
ce
n
at
u
r
e.
3
.
1
.
Nu
m
er
ica
l pa
rt
it
io
nin
g
a
nd
s
o
lutio
n pro
ce
du
re
s
3
.
1
.
1
.
Sp
a
t
ia
l
dis
cr
et
iza
t
io
n
T
h
e
co
m
p
u
tatio
n
al
d
o
m
a
in
was
d
is
cr
etize
d
in
to
o
r
d
er
ed
el
e
m
en
ts
o
f
th
e
d
iag
o
n
a
l
an
d
lo
n
g
it
u
d
in
a
l
d
ir
ec
tio
n
s
u
s
in
g
an
o
r
d
er
ed
g
r
id
o
f
×
n
o
d
es.
T
h
e
d
iag
o
n
al
co
o
r
d
in
ate
r
is
f
o
r
th
e
tr
an
s
v
er
s
e
d
ir
ec
tio
n
ac
r
o
s
s
th
e
t
h
ic
k
n
e
s
s
o
f
th
e
p
o
r
o
u
s
ch
a
n
n
el,
w
h
i
le
th
e
lo
n
g
it
u
d
in
al
co
o
r
d
i
n
ate
s
is
t
h
e
cu
r
v
ed
f
lo
w
p
at
h
.
T
h
e
s
p
atial
d
er
iv
ativ
e
s
in
th
e
m
o
m
en
tu
m
,
p
r
ess
u
r
e
g
r
ad
ie
n
t,
an
d
en
er
g
y
eq
u
a
tio
n
s
w
er
e
tak
en
f
i
n
ite
-
d
if
f
er
e
n
ce
f
o
r
m
s
to
ap
p
r
o
x
i
m
ate
as
i
n
[
1
9
]
,
[
2
0
]
.
T
h
e
ce
n
ter
d
if
f
er
en
ce
ap
p
r
o
x
im
a
tio
n
s
w
er
e
u
s
ed
at
d
if
f
u
s
io
n
b
o
u
n
d
ar
ies,
an
d
co
n
v
ec
tio
n
b
o
u
n
d
ar
ies
w
er
e
tr
ea
ted
b
y
a
b
iased
s
tab
le
d
if
f
er
en
tial
f
o
r
m
u
la
to
m
i
n
i
m
ize
n
o
n
p
h
y
s
ical
o
s
cil
latio
n
s
u
n
d
er
h
i
g
h
in
er
t
ia,
p
o
r
e
r
esis
tan
ce
,
an
d
h
y
d
r
o
m
ag
n
etic
d
y
n
a
m
ics
[
1
9
]
.
T
h
e
b
o
u
n
d
ar
y
co
n
d
itio
n
s
o
f
s
u
b
s
ec
tio
n
2
.
4
w
er
e
ap
p
lied
d
ir
ec
tly
to
t
h
e
b
o
u
n
d
ar
y
n
o
d
es.
3
.
1
.
2
.
I
t
er
a
t
iv
e
c
o
up
lin
g
s
t
ra
t
eg
y
Fo
r
ea
ch
ch
i
ller
an
d
p
ar
a
m
ete
r
s
et,
th
e
m
o
m
en
t
u
m
eq
u
at
io
n
s
w
er
e
s
o
lv
ed
co
n
s
id
er
in
g
t
h
e
p
r
ess
u
r
e
g
r
ad
ien
t
to
o
b
tain
th
e
r
ad
ial
an
d
tan
g
e
n
tial
v
elo
cit
y
co
m
p
o
n
en
t
s
.
T
h
e
v
elo
cit
y
f
ield
i
n
th
e
e
n
er
g
y
eq
u
atio
n
w
a
s
u
s
ed
to
ca
lcu
late
t
h
e
te
m
p
er
at
u
r
e
d
is
tr
ib
u
t
io
n
.
T
h
e
h
y
d
r
o
d
y
n
a
m
ic
an
d
t
h
er
m
al
s
o
lu
tio
n
s
w
er
e
co
u
p
led
th
r
o
u
g
h
a
n
ex
ter
n
al
iter
ati
v
e
l
o
o
p
s
in
ce
th
e
en
er
g
y
eq
u
atio
n
h
ad
co
n
v
ec
tio
n
,
d
if
f
u
s
io
n
,
atm
o
s
p
h
er
ic
h
ea
tin
g
,
v
is
co
s
it
y
d
is
s
ip
atio
n
,
an
d
v
o
lu
m
et
r
ic
h
ea
t
g
e
n
er
atio
n
b
o
u
n
d
a
r
ies
[
1
9
]
,
[
2
0
]
.
Dev
iatio
n
m
iti
g
atio
n
w
as
ap
p
lied
in
th
o
s
e
ca
s
e
s
w
h
er
e
it
w
a
s
n
e
ed
ed
to
en
s
u
r
e
th
at
th
e
s
o
l
u
tio
n
r
e
m
ai
n
ed
m
o
n
o
to
n
icall
y
co
n
v
er
g
en
t
an
d
h
en
ce
av
o
id
ed
an
y
n
u
m
er
ical
i
n
s
tab
ilit
y
th
at
m
ig
h
t
ar
i
s
e
d
u
e
to
t
h
e
co
m
b
in
ed
e
f
f
ec
ts
o
f
c
u
r
v
a
tu
r
e,
p
o
r
e
r
esis
tan
ce
,
an
d
m
a
g
n
et
ic
d
a
m
p
in
g
.
T
h
e
n
u
m
er
ical
p
r
o
ce
d
u
r
e
ap
p
l
ied
in
th
e
s
i
m
u
latio
n
is
b
r
ief
l
y
d
escr
ib
ed
as f
o
llo
w
s
:
Step
1
: Sp
ec
if
y
t
h
e
ch
a
n
n
el
g
e
o
m
e
tr
y
,
p
r
o
p
er
ties
o
f
th
e
co
o
lan
t,
p
ar
a
m
eter
s
o
f
t
h
e
p
o
r
o
u
s
m
ed
iu
m
,
p
ar
am
eter
o
f
t
h
e
m
ag
n
etic
f
iel
d
,
an
d
th
e
th
er
m
al
b
o
u
n
d
ar
y
c
o
n
d
itio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4864
S
o
ftw
a
r
e
s
imu
la
tio
n
o
f m
a
g
n
et
o
h
yd
r
o
d
y
n
a
mic
co
o
lin
g
flo
w
in
cu
r
ve
d
…
(
Ha
s
s
a
n
Mo
h
a
mm
a
d
Ha
s
s
a
n
)
663
Step
2
:
T
h
e
g
o
v
er
n
in
g
eq
u
atio
n
s
ar
e
d
is
cr
etize
d
in
t
h
e
r
an
d
s
d
ir
ec
tio
n
s
.
Step
3
: I
n
itialize
th
e
v
elo
cit
y
,
p
r
ess
u
r
e
g
r
ad
ien
t a
n
d
te
m
p
er
a
tu
r
e
f
ield
s
to
th
e
g
i
v
e
n
v
al
u
es
o
f
in
let
a
n
d
b
o
u
n
d
ar
y
co
n
d
itio
n
s
.
Step
4
: A
p
p
l
y
iter
ati
v
e
m
eth
o
d
s
to
s
o
lv
e
th
e
d
is
cr
etize
d
r
ad
ial
an
d
tan
g
en
tial
m
o
m
e
n
t
u
m
eq
u
atio
n
s
f
o
r
a
g
iv
e
n
r
ad
ial
p
o
s
itio
n
.
Step
5
: D
eter
m
in
e
t
h
e
p
r
ess
u
r
e
g
r
ad
ien
t r
elatio
n
s
b
y
th
e
co
n
v
er
g
en
t
m
o
m
en
tu
m
eq
u
i
lib
r
iu
m
eq
u
atio
n
.
Step
6
: Co
m
p
u
te
t
h
e
s
o
l
u
tio
n
o
f
th
e
d
is
cr
etize
d
en
er
g
y
eq
u
a
tio
n
w
it
h
th
e
i
n
itia
lized
v
elo
cit
y
an
d
th
e
p
r
ess
u
r
e
g
r
ad
ien
t f
ield
s
.
Step
7
: Rep
ea
t th
e
t
w
o
-
s
o
lu
t
io
n
p
r
o
ce
d
u
r
e
u
n
til b
o
th
h
y
d
r
o
d
y
n
a
m
ic
a
n
d
th
er
m
al
r
esid
u
e
s
m
ee
t t
h
e
s
tip
u
lated
co
n
v
er
g
e
n
ce
cr
iter
i
o
n
.
Step
8
: P
o
s
tp
r
o
ce
s
s
v
elo
cit
y
,
p
r
ess
u
r
e,
a
n
d
te
m
p
er
at
u
r
e
f
ield
s
an
d
co
n
tr
ast b
eh
a
v
io
r
f
o
r
w
a
ter
,
h
eliu
m
,
Pb
-
1
7
L
i,
an
d
P
b
-
1
7
L
i+AlN
n
p
s
.
3
.
1
.
3
.
Co
nv
er
g
ence
a
nd
s
t
a
bil
it
y
cr
it
er
ia
C
o
n
v
er
g
e
n
ce
o
f
th
e
n
u
m
er
ica
l
s
o
lu
tio
n
w
a
s
m
o
n
i
to
r
ed
w
it
h
s
ca
led
r
esid
u
als
f
o
r
th
e
v
el
o
cit
y
an
d
te
m
p
er
atu
r
e
f
ield
s
.
T
h
e
iter
a
tio
n
p
r
o
ce
s
s
en
d
ed
w
it
h
r
esi
d
u
als
u
n
d
er
ac
ce
p
tab
le
to
ler
an
ce
an
d
w
h
en
n
o
s
ig
n
i
f
ica
n
t
c
h
an
g
es
i
n
t
h
e
co
n
to
u
r
f
ield
a
n
d
li
n
e
p
r
o
f
ile
s
w
er
e
d
etec
ted
.
S
k
e
w
co
r
r
ec
ti
o
n
w
as
ap
p
lied
i
f
n
ee
d
ed
,
to
en
h
an
ce
t
h
e
n
u
m
er
ical
s
tab
ilit
y
,
also
f
o
r
s
t
r
o
n
g
Fo
r
ch
h
ei
m
er
r
esis
ta
n
ce
o
r
lar
g
e
m
a
g
n
et
ic
in
ter
ac
tio
n
.
Fi
n
all
y
,
a
ze
r
o
-
g
r
ad
ien
t
o
u
tp
u
t
co
n
d
it
io
n
w
a
s
e
n
f
o
r
ce
d
s
o
th
at
t
h
e
v
e
lo
cit
y
a
n
d
te
m
p
er
atu
r
e
f
ield
s
co
u
ld
leav
e
th
e
co
m
p
u
tat
io
n
al
d
o
m
ai
n
as a
n
o
r
m
al
o
u
t
f
lo
w
with
o
u
t a
r
ti
f
icia
l n
u
m
er
ical
s
tr
a
i
n
i
n
g
.
3
.
1
.
4
.
G
rid inde
pend
e
nce
a
n
d nu
m
er
ica
l v
er
if
ica
t
io
n
W
e
also
test
ed
g
r
id
in
d
ep
en
d
e
n
ce
to
en
s
u
r
e
t
h
at
th
e
ca
lc
u
lat
ed
th
er
m
al
r
esp
o
n
s
e
w
as
n
o
t
i
n
f
lu
e
n
ce
d
b
y
s
p
atial
r
eso
lu
tio
n
.
T
h
r
ee
s
tr
u
ctu
r
ed
g
r
id
s
o
f
d
i
m
en
s
io
n
s
4
0
×8
0
,
6
0
×1
2
0
,
an
d
8
1
×
1
6
1
w
er
e
test
ed
u
n
d
er
t
h
e
s
a
m
e
p
h
y
s
ical
p
ar
a
m
eter
s
a
n
d
b
o
u
n
d
ar
y
co
n
d
itio
n
s
.
As
an
i
n
d
icato
r
o
f
g
r
id
co
n
v
er
g
en
ce
,
th
e
d
im
e
n
s
io
n
le
s
s
te
m
p
er
atu
r
e
Θ
at
th
e
m
id
-
c
h
a
n
n
el
lo
ca
tio
n
(
r
m
id
,
s
m
id
)
w
a
s
ch
o
s
en
.
T
ab
le
1
p
r
esen
ts
th
e
r
esu
lts
o
f
th
e
g
r
id
in
d
ep
en
d
en
ce
test
.
T
h
e
d
if
f
er
en
ce
b
et
w
ee
n
th
e
6
0
×1
2
0
an
d
8
1
×
1
6
1
g
r
id
s
is
alm
o
s
t
n
e
g
li
g
ib
le,
s
h
o
w
i
n
g
t
h
at
in
cr
ea
s
i
n
g
t
h
e
g
r
id
r
eso
lu
tio
n
h
as
litt
le
ef
f
ec
t
o
n
t
h
e
s
elec
t
ed
th
er
m
al
r
esp
o
n
s
e.
T
h
er
ef
o
r
e,
w
e
s
e
lecte
d
th
e
6
0
×1
2
0
g
r
id
f
o
r
u
s
e
i
n
later
s
i
m
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latio
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s
b
ec
au
s
e
it
p
r
o
v
id
es
a
g
o
o
d
b
alan
c
e
b
et
w
ee
n
n
u
m
e
r
ical
ac
cu
r
ac
y
a
n
d
co
m
p
u
tatio
n
al
co
s
t.
T
ab
le
1
.
Gr
id
-
in
d
ep
en
d
en
ce
s
t
u
d
y
b
ased
o
n
th
e
d
i
m
e
n
s
io
n
les
s
te
m
p
er
atu
r
e
ev
alu
ated
at
t
h
e
m
id
-
c
h
a
n
n
el
lo
ca
tio
n
(
,
)
G
r
i
d
(
×
)
Θ
(
,
)
R
e
l
a
t
i
v
e
d
i
f
f
e
r
e
n
c
e
(
%)
40
×
80
1
.
1288476266
×
10
−
11
N
/
A
60
×
120
1
.
1688476742
×
10
−
11
3
.
4
2
81
×
161
1
.
1688476970
×
10
−
11
1
.
95
×
10⁻
⁶
3
.
2
.
Nu
m
er
ica
l v
er
if
ica
t
io
n a
nd
v
a
lid
a
t
io
n o
f
t
he
bo
un
da
ry
s
t
a
t
e
T
h
e
n
ex
t
n
u
m
er
ical
tes
t
w
as
ca
r
r
ied
o
u
t
to
f
u
r
th
er
co
n
f
ir
m
t
h
e
r
eliab
ilit
y
o
f
t
h
e
f
in
ite
-
d
if
f
er
en
ce
s
i
m
u
lat
io
n
.
T
h
e
r
esu
lts
o
f
g
r
id
in
d
ep
en
d
en
ce
in
T
ab
le
1
w
er
e
u
s
ed
,
f
ir
s
t
to
esti
m
ate
t
h
e
r
el
ativ
e
d
i
m
e
n
s
io
n
le
s
s
te
m
p
er
atu
r
e
v
ar
iatio
n
in
th
e
m
id
d
le
o
f
t
h
e
c
h
an
n
el
b
et
w
e
en
s
u
cc
es
s
i
v
e
g
r
id
o
p
ti
m
izati
o
n
s
.
T
h
e
r
elativ
e
d
if
f
er
e
n
ce
b
et
w
ee
n
4
0
×8
0
an
d
6
0
×1
2
0
g
r
id
s
w
a
s
ab
o
u
t
3
.
4
2
%;
th
at
b
et
w
ee
n
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0
×1
2
0
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d
8
1
×1
6
1
g
r
id
s
w
a
s
ab
o
u
t
1
.
9
5
×1
0
⁻⁶%.
T
h
is
v
er
y
s
m
al
l
d
if
f
er
en
ce
b
et
w
ee
n
t
h
e
t
w
o
f
i
n
est
g
r
id
s
co
n
f
ir
m
s
t
h
at
th
e
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h
o
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en
6
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×1
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0
g
r
id
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i
v
es
g
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ep
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en
t r
e
s
u
lt
s
f
o
r
t
h
e
th
er
m
al
f
ield
at
a
r
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s
o
n
ab
le
co
m
p
u
tatio
n
al
co
s
t
.
T
h
e
s
ec
o
n
d
v
alid
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n
w
as
d
o
n
e
b
y
s
t
u
d
y
i
n
g
t
h
e
p
h
y
s
ical
b
eh
av
io
u
r
o
f
th
e
g
o
v
er
n
i
n
g
m
o
d
el
w
h
e
n
th
e
c
u
r
v
at
u
r
e
e
f
f
ec
t
is
w
ea
k
e
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ed
.
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n
th
i
s
ca
s
e,
t
h
e
lo
ca
l r
ad
iu
s
b
o
u
n
d
ar
y
ass
o
ciate
d
w
i
th
th
e
cu
r
v
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co
o
r
d
in
ate
s
y
s
te
m
te
n
d
s
to
w
ar
d
th
e
co
r
r
esp
o
n
d
in
g
s
tr
aig
h
t
ch
a
n
n
el
b
eh
av
io
u
r
,
an
d
th
e
ef
f
ec
t
o
f
th
e
c
en
tr
if
u
g
al
f
o
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ce
o
n
d
iag
o
n
al
m
o
m
en
tu
m
eq
u
ilib
r
i
u
m
b
ec
o
m
es
les
s
s
i
g
n
i
f
ica
n
t.
I
t
w
as
also
n
u
m
er
icall
y
p
r
o
v
e
d
th
at
u
n
d
er
w
ea
k
b
en
d
in
g
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n
d
itio
n
s
,
t
h
er
e
is
a
d
ec
r
ea
s
e
in
th
e
r
ad
ial
v
elo
cit
y
co
m
p
o
n
e
n
t
co
m
p
ar
ed
to
th
e
ta
n
g
en
t
ial
co
m
p
o
n
e
n
t
,
w
h
ic
h
is
co
n
s
is
te
n
t
w
it
h
t
h
e
ex
p
ec
ted
d
ec
r
ea
s
e
in
s
ec
o
n
d
ar
y
m
o
tio
n
d
u
e
to
b
e
n
d
in
g
.
T
h
ir
d
,
th
e
in
d
i
v
id
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al
p
h
y
s
ical
b
o
u
n
d
ar
ies
w
er
e
c
h
ec
k
ed
b
y
f
i
r
s
t r
ed
u
ci
n
g
th
e
m
a
in
s
o
u
r
ce
b
o
u
n
d
ar
ies
in
s
ep
ar
ate
n
u
m
er
ical
e
x
p
er
i
m
en
ts
.
T
h
e
m
ag
n
etic
i
n
ter
ac
tio
n
co
ef
f
icie
n
t
w
a
s
r
ed
u
ce
d
,
an
d
th
is
w
ea
k
e
n
ed
th
e
L
o
r
en
tz
f
o
r
ce
d
a
m
p
in
g
,
w
h
il
e
th
e
co
n
d
u
ctiv
e
co
o
lan
t
w
as
s
ee
n
to
h
av
e
h
i
g
h
er
v
elo
cit
y
[
1
3
]
–
[
1
5
]
.
Dar
cy
-
Fo
r
ch
h
ei
m
er
r
esi
s
tan
ce
b
o
u
n
d
ar
ies
w
er
e
r
ed
u
ce
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to
r
ef
le
ct
th
e
p
r
ess
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r
e
g
r
ad
ie
n
t
co
n
d
itio
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,
w
h
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ei
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t
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r
esis
ta
n
ce
o
f
th
e
p
o
r
o
u
s
m
ed
i
u
m
is
r
ed
u
ce
d
[
8
]
–
[
1
2
]
.
T
h
ese
b
o
u
n
d
ar
y
r
esp
o
n
s
es
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in
lin
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w
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4.
RE
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Her
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elate
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Stu
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1.
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Fig
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[
6
]
–
[
8
]
th
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in
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tial
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ch
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els [
8
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–
[
1
2
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.
4.
2
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Fig
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[
8
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–
[
1
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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Evaluation Warning : The document was created with Spire.PDF for Python.