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SWIFT
SWIFTsim
Commits
edf1eb93
Commit
edf1eb93
authored
May 08, 2020
by
Matthieu Schaller
Browse files
Be more explicit about the softened expressions in the theory document
parent
77463e70
Changes
1
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theory/Multipoles/potential_softening.tex
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edf1eb93
...
...
@@ 51,9 +51,10 @@ r^{3} & \mbox{if} & r \geq H,
\end{align}
with
$
g
(
u
)
\equiv
f'
(
u
)/
u
=

21
u
^
5
+
90
u
^
4

140
u
^
3
+
84
u
^
2

14
$
. This last
expression has the advantage of not containing any divisions or
branching, making it faster to evaluate than the softened force
derived from the
\cite
{
Monaghan1985
}
spline kernel. Note also, the
useful expression for the norm of the forces:
branching (besides the always necessary check for
$
r<H
$
), making it
faster to evaluate than the softened force derived from the
\cite
{
Monaghan1985
}
spline kernel. Note also, the useful expression
for the norm of the forces:
\begin{align}

\mathbf
{
\nabla
}
\varphi
(r,H) =
\left\lbrace
\begin{array}
{
rcl
}
...
...
@@ 68,8 +69,6 @@ resulting forces are shown on Fig. \ref{fig:fmm:softening} (for more
details about how these are constructed see section 2
of~
\cite
{
Price2007
}
). For comparison purposes, we also implemented the
more traditional splinekernel softening in
\swift
.
\begin{figure}
\includegraphics
[width=\columnwidth]
{
potential.pdf
}
\caption
{
The density (top), potential (middle) and forces (bottom)
...
...
@@ 81,3 +80,9 @@ more traditional splinekernel softening in \swift.
potential at
$
r
=
H
$
to better highlight the differences in shapes.
}
\label
{
fig:fmm:softening
}
\end{figure}
Users specify the value of the Plummerequivalent softening
$
\epsilon
_{
\rm
Plummer
}$
in the parameter file.
\subsubsection
{
Interaction of bodies with different softening lengths
}
\textcolor
{
red
}{
MORE WORDS HERE.
}
\\
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