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The gravitational potential entering in the source terms of the Navier-Stokes equations is the sum of multiple terms:
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The gravitational potential entering in the source terms of the Navier-Stokes equations is the sum of multiple terms:
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1. ##The potential from the central massive body (primary of mass $`M_*`$):
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## The potential from the central massive body (primary of mass $`M_*`$):
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$`\Phi_*=-{{ G M_*} \over {r}}`$
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$`\Phi_*=-{{ G M_*} \over {r}}`$
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2. ##The potential form the planets of mass $m_p$.
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## The potential form the planets of mass $m_p$.
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Below we consider the case of one single planet, easily extended to multiple planets.
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Below we consider the case of one single planet, easily extended to multiple planets.
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- In the 3 Dimensional case
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- In the 3 Dimensional case
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we use a cubic-potential of the form:
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we use a cubic-potential of the form:
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... | @@ -54,7 +54,7 @@ To select this choice for a simulation in the config file: |
... | @@ -54,7 +54,7 @@ To select this choice for a simulation in the config file: |
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}
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}
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```
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```
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3. ##The indirect terms
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## The indirect terms
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This term in the potential accounts for the acceleration of the primary
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This term in the potential accounts for the acceleration of the primary
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