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SWIFT
SWIFTsim
Commits
451dfabc
Commit
451dfabc
authored
6 years ago
by
Matthieu Schaller
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Make the anarchy SPH latex document compile.
parent
e1e77b67
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theory/SPH/Flavours/anarchy.tex
+2
-2
2 additions, 2 deletions
theory/SPH/Flavours/anarchy.tex
with
2 additions
and
2 deletions
theory/SPH/Flavours/anarchy.tex
+
2
−
2
View file @
451dfabc
...
@@ -108,7 +108,7 @@ their time-integration. The following quantities are calculated:
...
@@ -108,7 +108,7 @@ their time-integration. The following quantities are calculated:
\mu
_{
ij
}
(
b
_
i
+
b
_
j
)
(
\nabla
_
i W
_
i
+
\nabla
_
j W
_
j
)/
(
\rho
_
i
+
\rho
_
j
)
$
\mu
_{
ij
}
(
b
_
i
+
b
_
j
)
(
\nabla
_
i W
_
i
+
\nabla
_
j W
_
j
)/
(
\rho
_
i
+
\rho
_
j
)
$
\item
$
\dot
{
u
}_{
ij,
{
\rm
hydro
}}
=
\sum
_
j m
_
j u
_
i u
_
j
(
\gamma
-
1
)
^
2
\item
$
\dot
{
u
}_{
ij,
{
\rm
hydro
}}
=
\sum
_
j m
_
j u
_
i u
_
j
(
\gamma
-
1
)
^
2
\frac
{
f
_{
ij
}}{
\bar
{
P
}_
i
}
\nabla
_
i W
_
i
$
\frac
{
f
_{
ij
}}{
\bar
{
P
}_
i
}
\nabla
_
i W
_
i
$
\item
$
\dot
{
u
}_{
ij,
{
\rm
visc
}}
=
\frac
{
1
}{
2
}
\
a
_{
\rm
visc
}
(
\mathbf
{
v
}_{
ij
}
\cdot
\tilde
{
\mathbf
{
x
}}_{
ij
}
+
r
^
2
a
^
2
H
)
$
\item
$
\dot
{
u
}_{
ij,
{
\rm
visc
}}
=
\frac
{
1
}{
2
}
a
_{
\rm
visc
}
(
\mathbf
{
v
}_{
ij
}
\cdot
\tilde
{
\mathbf
{
x
}}_{
ij
}
+
r
^
2
a
^
2
H
)
$
\item
$
v
_{{
\rm
diff
}
, i
}
=
{
\rm
max
}
(
0
, c
_
i
+
c
_
j
+
\mathbf
{
v
}_{
ij
}
\cdot
\tilde
{
\mathbf
{
x
}}_{
ij
}
+
r
^
2
a
^
2
H
)
$
\item
$
v
_{{
\rm
diff
}
, i
}
=
{
\rm
max
}
(
0
, c
_
i
+
c
_
j
+
\mathbf
{
v
}_{
ij
}
\cdot
\tilde
{
\mathbf
{
x
}}_{
ij
}
+
r
^
2
a
^
2
H
)
$
\item
$
\dot
{
u
}_{
ij,
{
\rm
diff
}}
=
\frac
{
1
}{
2
}
(
\tilde
{
\alpha
}_
i
+
\tilde
{
\alpha
}_
j
)
a
^{
(
3
\gamma
-
5
)/
2
)
}
\item
$
\dot
{
u
}_{
ij,
{
\rm
diff
}}
=
\frac
{
1
}{
2
}
(
\tilde
{
\alpha
}_
i
+
\tilde
{
\alpha
}_
j
)
a
^{
(
3
\gamma
-
5
)/
2
)
}
v
_{{
\rm
diff
}
, i
}
(
u
_
i
-
u
_
j
)
(
\nabla
_
i W
_
i
+
\nabla
_
j W
_
j
)/
(
\rho
_
i
+
\rho
_
j
)
$
v
_{{
\rm
diff
}
, i
}
(
u
_
i
-
u
_
j
)
(
\nabla
_
i W
_
i
+
\nabla
_
j W
_
j
)/
(
\rho
_
i
+
\rho
_
j
)
$
...
@@ -118,6 +118,6 @@ where:
...
@@ -118,6 +118,6 @@ where:
\begin{itemize}
\begin{itemize}
\item
$
f
_{
ij
}$
are the variable smoothing length correction factors
\item
$
f
_{
ij
}$
are the variable smoothing length correction factors
\item
$
b
_
i
$
is the Balsara switch for particle
$
i
$
\item
$
b
_
i
$
is the Balsara switch for particle
$
i
$
\item
$
\mu
_{
ij
}
=
a
^{
(
3
\gamma
-
5
)/
2
)
{
\rm
min
}
(
\mathbf
{
v
}_{
ij
}
\cdot
\tilde
{
\mathbf
{
x
}}_{
ij
}
+
r
^
2
a
^
2
H,
0
)
$
\item
$
\mu
_{
ij
}
=
a
^{
(
3
\gamma
-
5
)/
2
}
{
\rm
min
}
(
\mathbf
{
v
}_{
ij
}
\cdot
\tilde
{
\mathbf
{
x
}}_{
ij
}
+
r
^
2
a
^
2
H,
0
)
$
\end{itemize}
\end{itemize}
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