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SWIFT
SWIFTsim
Commits
4a58893a
Commit
4a58893a
authored
Oct 25, 2012
by
Matthieu Schaller
Browse files
Corrected a few typos in the latex document.
Formercommitid: e9567f4ffdde605b320736473eea9d16d40e93c1
parent
41c8de38
Changes
1
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theory/latex/sph.tex
View file @
4a58893a
...
...
@@ 71,7 +71,7 @@ Coming back to the simplest case, the derivatives of the kernel function are giv
\begin{eqnarray*}
\vec\nabla
W(
\vec
{
x
}
,h)
&
=
&
\frac
{
1
}{
h
^
4
}
f'
\left
(
\frac
{

\vec
{
x
}

}{
h
}
\right
)
\frac
{
\vec
{
x
}}{

\vec
{
x
}

}
\\
\frac
{
\partial
W(
\vec
{
x
}
,h)
}{
\partial
h
}
&
=
&

\frac
{
1
}{
h
^
4
}
\left
[3
\left
(
\frac
{

\vec
{
x
}

}{
h
}
\right
) +
\frac
{
\partial
W(
\vec
{
x
}
,h)
}{
\partial
h
}
&
=
&

\frac
{
1
}{
h
^
4
}
\left
[3
f
\left
(
\frac
{

\vec
{
x
}

}{
h
}
\right
) +
\frac
{

\vec
{
x
}

}{
h
}
f'
\left
(
\frac
{

\vec
{
x
}

}{
h
}
\right
)
\right
]
\end{eqnarray*}
...
...
@@ 163,11 +163,16 @@ The time step is then given by the Courant relation:
\Delta
t
_
i = C
_{
CFL
}
\frac
{
h
_
i
}{
c
_
i
}
\end{equation}
where the CFL parameter usually takes a value between
$
0
.
1
$
and
$
0
.
3
$
. The integration in time can then take place. The
where the CFL parameter usually takes a value between
$
0
.
2
$
and
$
0
.
3
$
. The integration in time can then take place. The
leapfrog integrator is usually used as it behaves well when coupled to gravity.
\\
In the case where only one global timestep is used for all particles, the minimal timestep of all particles is reduced
and used.
and used.
\\
Notice that
$
h
$
has to be recomputed through the iterative process
presented in the previous section at every timestep. The time
derivative of the smoothing length only give a rough estimate of its
change. It only provides a good guess for the NewtonRaphson (or
bissection) scheme.
\section
{
Conserved quantities
}
...
...
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