The gravitational potential entering in the source terms of the Navier-Stokes equations is the sum of multiple terms:
## The potential from the central massive body (primary of mass $`M_*`$):
## The potential from the central massive body
Considering a primary of mass $`M_*`$:
$`\Phi_*=-{{ G M_*} \over {r}}`$
## The potential form the planets of mass $m_p$.
Below we consider the case of one single planet, easily extended to multiple planets.
## The potential form the planets
Below we consider the case of one single planet of mass $m_p$ (it is easily extended to multiple planets).
- In the 3 Dimensional case
we use a cubic-potential of the form:
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@@ -57,7 +58,10 @@ To select this choice for a simulation in the config file:
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## The indirect terms
This term in the potential accounts for the acceleration of the primary
Two terms in the potential accounts for the acceleration of the primary they come from the acceleration due respectively to the planet(s) and to the disk:
$`\tilde \Phi_p = {{ G m_p} \over {r_p^3}}(r_p\codot r)`$
