Renewed theory, interfacing, and visualization of thermal lattice Boltzmann schemes [Elektronische Ressource] / vorgelegt von Peter Michael Späth
144 Pages
English

Renewed theory, interfacing, and visualization of thermal lattice Boltzmann schemes [Elektronische Ressource] / vorgelegt von Peter Michael Späth

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Published 01 January 2000
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Renew
ed
Theory
,
v

(TU
In
Sp
terfacing,
h
and

Visualization
P
of
am
Thermal
t
Lattice
(TU
Boltzmann
(Univ
Sc
der
hemes
Dipl.-Ph
v

on
geb
der
in
F

akult
26.1.2000
at
Prof.Dr.K.H.
f
Dr.H.-R.

Prof.Dr.W.
ur
at

T
haften
erteidigung:
der
on

ys.

eter
hen
hael
Univ
ath
ersit
oren
at
11.11.1969
Chemnitz
W
genehmigte
urzburg
Dissertation
h
zur
am
Erlangung

des
ter:
ak
Homann

Chemnitz)
hen
Berger
Grades
Chemnitz)
Do
Kinzel

ersit
rerum
W
naturalium
urzburg)
Dr.rer.nat.
ag
v
V
orgelegt
14.6.2000

In
this
Doktor
terpreter
del
giv
arb
the
eit
An
the
een
Lattice
realized
Boltzmann
of
sc
is
heme,
ted
a
unication

b
metho

d

for
h
the
sc
sim
for
ulation
presen
of

o
tation
ws
with
in
et


b
an
oundaries,

is
from
in
in
v
unication.
estigated.

Its
applicabilit
theory
Lattice
is
to
re-
o
new
temp
ed
are
b
ted.
y
ob
emphasizing
orien
the
implemen
en
is
trop
en
y

maximization
b

w
and
ob
new
realized
means
y
for
in
the
ob
mo
and
deling
unication
of
outside
geometries
via
(including
terpro
mo

ving
Within
b
new
oundaries)

and
the
the
y
visual
existing
repreBoltzmann
sen
hemes
tation
mo
of
thermal
ev
ws
oluting
arbitrary
o
eratures
ws
reexamined.Con
ten
ts
.
2
.
1
.
In
.
tro
Flo

.
4
.
1.1
.

The
Sc
ws
hemes
1.3.7
in
.
Fluid
.

Fluid
.
of
.
a
.
.
.
.
.
ery
.
1.3.5
.
.
.
.
.
.
.
Lattice
.
.
.
.
.
.
.
.
.
.
4
.
1.1.1
.
Lo
w

.
Thermo
The

.
Equilibrium
En
.
.
.
.
.
vier
.
.
.
{
.
.
.

.
.
.
.
.
Bol
.
.
.
Computation
.
Sc
5
.
1.1.2
.
Dieren
.
t
The

.
Mo
.
dels
.
.
.
.
.
.
.
.
.
.
The
.
.
.
.
.
of
.
T
.
.
.
.
.
.
.
of
.
.
.
.
.
.
6
the
1.2
.
Lattice
.
Gas
En
Sc
44
hemes
the
.
Stokes
.
.
.
.
.
in
.
tzmann
.
.
.
.
.
1.3.6
.
Bol
.
.
.
.
.
.
.
.
.
Lattice
.
Sc
.
.
.
.
.
36
.
in
.
Bol
.
.
.
.
.
.
.
.
.
.
8
.
1.2.1
.
The
37
HPP
trop
Lattice
.
Gas
.
.
.
.
.
.
.
.
.
.
.
.
1.4.1
.
trop
.
.
.
.
.
.
.
.
.
.
.
38
.
La
.

.
.
.
.
.
.
.
New
.
Boltzmann
9
2.1
1.2.2
erature
Other
Gas
Lattice
.
Gas
.
Mo
.
dels
.
.
42
.
trop
.
LB
.
.
.
.
.
.
.
.
.
.
.
43
.
y
.
Space'
.
.
.
.
.
.
.
43
.
Distribution
.
y
.
.
17
v
1.2.3
of
Boundaries
Na
in
{
Lattice
Equation
Gases
.
.
.
.
.
.
29
.
Boundaries
.
Lattice
.
Bol
.
Flo
.
.
.
.
.
.
.
.
.
31
.
F
.
Lattice
.
tzmann
.
ws
.
.
19
.
1.2.4
.
Lattice-Gas
.
F
.

.
Flo
34
ws
Thermal
.
{
.
tzmann
.
hemes
.
.
.
.
.
.
.
.
.
.
.
1.3.8
.
Steps
.
the
.
{
.
tzmann
.
heme
.
.
.
.
.
.
.
.
21
.
1.2.5
.
Thermal
.
Lattice
.
Gases
.
.
.
.
.
.
.
.
.
.
.
.
1.4
.
En
.
y
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
22
.
1.3
.
Lattice
38
Boltzmann
The
Sc
En
hemes:
y
T
.
raditional
.
T
.
reatmen
.
t
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1.4.2
.

23
w
1.3.1
Thermo
The
.
Lattice
.
Bol
.
tzmann
.
Equation
.
.
.
.
39
.
The
.
Theory
.
Lattice
.
Flo
.
42
.
The
.
emp
.
of
.
LB
.
.
.
.
25
.
1.3.2
.
The
.
Linearized
.
Collision
.
Op
.
erator
.
.
.
.
2.2
.
En
.
y
.
a
.
Gas
.
.
.
.
.
.
.
.
.
.
.
.
.
.
26
.
1.3.3
.
The
.
Equilibrium
.
Distribution
2.2.1
.
trop
.
in
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2.3
.
Equilibrium
.
from
.
trop
.
Maximization
28
.
1.3.4
.

1
2.3.1
Order-0
P
Messaging
.
.
arameter
.
Expansion
.
.
.
.
.
.
.
.
.
.
BoundaryMap
.
.
.
.
.
.
.
.
.
3.4
.
71
.
.
.
.
.
.
.
.
.
76
46
.
2.3.2
.
Order-1
.
P
.
arameter
.
Expansion
.
.
Prosp
.
.
.
.
.
.
.
.
.
.
.
.
.
3.4.3
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
46
.
2.3.3
.
The
.
Equilibrium
.
Distribution:
.
Summary
.
.
File
.
86
.
.
.
3.8
.
.
.
.
.
Momen
.
.
.
.
.
.
48
.
2.3.4
.
Prop
.
erties
.
of
.
Dieren
.
t
74
Lattice
.
Geometries
.
.
.
.
.
.
.
.
.
.
3.4.4
.
.
.
.
.
.
.
.
49
.
2.4
.
The
.

.
Square
.
Lattice
.
.
.
.
.
.

.
.
.
.
.
View
.
.
.
.
.
.
.
Sending
.
.
.
.
.
.
.
.
.
.
.
84
.
.
.
.
52
.
2.4.1
.
Equilibrium
.
Distribution
.
.
ork
.
.
.
.
.
.
.
Summary
.
The
.
99
.
.
.
.
.
.
.
.
.
Main
.
.
.
.
.
.
.
.
.
.
.
.
.
.
52

2.4.2
.
Implemen
.
tation
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
FieldMap
.
.
.
.
.
.
.
.
.
.
.
.
.
FieldMapExt
.
.
.
.
.
.
.
.
.
.
.
3.4.5
53
.
2.5
.
The
.
13-Directional
.
T
.
riangular
75
Lattice
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
77
.
.
.
.
.
.
53
.
2.5.1
.
Equilibrium
3.5
Distribution
Class
.
.
.
.
.
.
.
.
.
.
.
.
.
78
.
to
.
.
.
.
.
.
.
.
.
.
.
3.6.1
.
'send'
.
.
.
.
.
.
.
.
53
The
2.5.2
'op
Implemen
.
tation
.
.
.
.
Sample
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
uture
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
91
.
F
.
94
.
Equilibrium
.
Compar.
.
.
.
54
.
2.5.3
.
A
.
Simple
.
P
.
anel
.
Application
69
.
The
.
Class
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
3.4.1
56
Geometry
2.5.4
.
The
.
Sp
.

.
Heat
.
Conductivit
.
y
.
.
.
.
.
.
.
.
.
.
.
.
3.4.2
.
Equilibrium
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
61
.
2.5.5
.
The
.
Viscosit
74
y

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
74
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
64
75
2.6

External
.
F
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
3.4.6
.
STRAlattice
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
3.4.7
.
FieldManager
.
.
.
.
.
.
.
.
.
.
65
.
2.7
.
Summary
.
.
.
.
.
.
.
.
3.4.8
.
BoundaryManager
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
77
.
The
.
er
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
66
3.6
3
Messages
t-LABOS,
'Main'
an
.
Ob
.

.
Orien
.
ted
.
LB
.
Solv
.
er
.
67
.
3.1
.
Utilit
84
y
Simple
Classes
via
and
.
Data
.
Classes
.
.
.
.
.
.
.
.
.
.
.
.
.
.
3.6.2
.
Program
.
Handler
.
erate'
.
.
.
.
.
.
.
.
.
.
.
.
.
3.7
.
Programs
68
.
3.2
.
Con
.
troling
.
from
.
Outside
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
86
.
F
.
W
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
68
.
3.3
.
The
4
In
and
terpreter
uture
Base
ects
Class
A
.
Lattice-Boltzmann
.
from
.
tum
.
ison
.
2B
The
Utilities

117
.
Class
.
Library
.
105
D.7
B.1
.

.
Bo
.
olean
.
.
122
.
BoundaryManager
.
E.2
.
129
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Geometry
.
.
.
Equilibrium
.
.
.
.
.
.
.
.
105
.
B.2
.

.
V
.
ec2D,
.

.
V
.
ec3D
.
.
125
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
'Main'
.
.
.
.
.
.
.
.
.
.
106
.
B.3
.

119
Plane
.
.
.
.
.
.
120
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
'View
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
108
ScalarField
B.4
.

.

.
.
.
.
.
.
.
.
.
.
E.5
.
.
.
.
.
.
.
E.6
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Classes
.
D.1
.
.
.
.
.
.
.
.
.
.
.
.
108
.
B.5
D.2

.
Area
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
121
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
109
.
B.6
.

.
Out
.
.
.
.
FieldManager
.
.
.
.
.
.
.
.
.
.
.
.
.
D.8
.
.
.
.
.
.
.
.
.
.
.
.
.
Classes
.
127
.
ort
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Putter
.
.
.
.
.
.
.
.
.
.
110
.
B.7
.

E.3
Streamline
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
OutWindo
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
View
.
.
.
.
.
.
.
.
111
.
C
.
The
.
Data
136
Class
.
Library
.
113
.
C.1
.

.
FieldP
.
oin
.
t
.
.
.
.
.
.
.
.
.
.
.
.
.
.
D
.
under
.
118
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
118
.

.
.
.
.
113
.
C.2
.

.
Distribution
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
D.3
.
FieldMap
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
D.4
.
FieldMapExt
.
.
113
.
C.3
.

.
No
.
de
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
D.5
.
BoundaryMap
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
D.6
.
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116
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C.8
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EdgeOb
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j
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3
Chapter
1
In
tro
hapter
Fluid
at

of
The

dev
and
elopmen
een
t
hemes
of
ian
sim
rev
ulation
1
sc
their
hemes
of
in
other
h
the
ydro
describ

The
has
ev
gained
detail.

equations
able
at
atten
appro
tion

within
elds.
the
an
last
whic

sub
One
ork
reason
is
is
hapters.
the
Fluids
inabilit
dieren
y
1.
of
usually
analytical
Here
sc
is
hemes

ev
means,
en
w
to
lead
solv
k
e
t
v
lev
ery
to
fundamen
ecomes
tal
are
problems.

Simply


giv
an
v
idealized


has

on
with
b
wind
the
blo
the
wing
rep
from
ted
fron
t
t-side

(Fig.1.1)
Fluid
-
b
one
on
will
lev
hardly
lev
nd
lev
but
lev
an
Hamil
appro
ersible
ximativ
motion
e
single
analytical
k
solution.
uously
But
monitored
there
ersibilit
is
b
a
the
n
time,
um
motion
b
the
er
2
of
the
n
1
u-
>

2.
sc
Here
hemes
is
with

the
description
abilit
ersible.
y

to
amined
solv
erties
e
the
this
tro
problem.

The
to
Lattice
e
Boltzmann
o
sc
erview
heme
the
describ
h
ed
h
in
b
this
done
rep
the
ort

is
y
among
authors;
the
w
latest
of
whic
author
h
this
ha
ort
v
presen
e
in
b
subsequen
een

dev
1.1
elop
Sc
ed
in
[31

,

25
e
,
ed
8,
three
40
t
,
els:
34

,
els:
35

,
el.
1

,
el
2].
exhibits

ton
h
rev
on
motion.
its
the
v
of
alidit
ery
y
particle
and
trac

ed
y
tin
is
and
still
are
in
in
adv
Rev

y
esp
that
ecially
y
when
ersing
it
arro

of
to
the
stabilit
of
y
uniquely
and
from
dealing
state
with
t
b

oundary
to

state
ditions.
t
This
for
is
2

t
in
.
most

of
el.
the
an
w
ximation
ork
applied
whic
the
h

is
the
published
b
on
irrev
the
Lo
sub
thermo

equilibria
It
exis
and
the
prop
aim
are
of
to
this

in
4? ?
?
wind
?? ?
mak
elo
eration
equilibration
go

Figure
if
1.1:
to
An
state
idealized


equilibration
and
faster
wind
from
blo

wing
an
from
ermeable
fron
p
t{righ
w
t.
friction
A

problem
explained
analytical
the
metho
no
ds

fail
a
to
from
handle.
ere
3.


.
lev
divide
el.
innitely
All
t
quan
from
tities
view,
are
same.


to
i.e.
b
the
e
ards

of
tin
as
uous
this
in
uc
space
et
and
if
time
th
and

only
illustrated

a
v
a
ariables
A
(suc
means
h
system
as
alone,
mass
w
densit
as
y
b
,
w
o
time
w
region
v

elo
but

alls.
y
this
,
es
temp
ph
erature)
t
app
the
ear
remains
in
ards
the
er,
description.

The
es

to
description
the
results
state
from
to
the
most

h
lev

el
y
resp
b
ectiv
No
ely

the
ens

faster
lev

el
een
b
ok
y
w
patc
alls,
hing
dev
together
a
v
of
olume
This
elemen
Fig.1.2.
ts
e
whic
dierence)
h
w
are
y

equilibrium.
to
way
b
equilibrium
e
that,
in
the
a
w
lo
left

the
thermo
state

ould
equilibrium.
hange
The
time
notion
es
of
y
the
No
equilibration
at
inside
y
those
sub
v
the
olume
in
elemen
small
ts
with
taking
thin
place
imp
m
w
uc
A
h