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Update Gravitational Potential including indirect terms
authored
Apr 28, 2021
by
Elena Lega
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Code-equations/Gravitational-Potential-including-indirect-terms.md
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@@ -8,14 +8,14 @@ The gravitational potential entering in the source terms of the Navier-Stokes eq
we use a cubic-potential of the form:
$
`\Phi _p = \left\lbrace \begin{array}{ll}
-{m_pG\over d} & d > r_{\rm sm} \\
-{m_pG\over d} & d > r_{\rm sm}
}
\\
-{m_pG\over d}f({d\over r_{\rm sm}}) & d\leq r_{\rm sm}
\end{array} \right.`
$
with $
`f({d\over r_{\rm sm}}) = \left [ \left( {d\over r_{\rm sm}}\right)^4-2\left( {d\over r_{\rm sm}}\right)^3+2{d\over r_{\rm sm}} \right]`
$;
$
`d`
$ is the distance from the disc element to the planet, and $
`r_{\rm sm}`
$ the
smoothing length:
$
`r_{\rm sm} = \
alpha _{sm}
R_H`
$, where $
`\
alpha _{sm}
`
$ is a smoothing parameter and
$
`r_{\rm sm} = \
epsilon
R_H`
$, where $
`\
epsilon
`
$ is a smoothing parameter and
$
`R_H`
$ is the Hill radius of the planet.
To select this choice for a simulation in the config file:
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