| 4 |
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| 5 |
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| 6 |
\subsection{Non-linear free surface} |
\subsection{Non-linear free surface} |
| 7 |
|
\label{sect:nonlinear-freesurface} |
| 8 |
|
|
| 9 |
Recently, two options have been added to the model (and have not yet |
Recently, two options have been added to the model (and have not yet |
| 10 |
been extensively tested) that concern the free surface formulation. |
been extensively tested) that concern the free surface formulation. |
| 32 |
easily be incorporated in $\Phi'_{hyd}$. |
easily be incorporated in $\Phi'_{hyd}$. |
| 33 |
|
|
| 34 |
For the atmosphere, however, because of topographic effects, the |
For the atmosphere, however, because of topographic effects, the |
| 35 |
reference surface pressure $R_o$ has large spacial variations that |
reference surface pressure $R_o$ has large spatial variations that |
| 36 |
are responsible for significant $b_s$ variations (from 0.8 to 1.2 |
are responsible for significant $b_s$ variations (from 0.8 to 1.2 |
| 37 |
$[m^3/kg]$). For this reason, we use a non-uniform linear coefficient |
$[m^3/kg]$). For this reason, we use a non-uniform linear coefficient |
| 38 |
$b_s$. |
$b_s$. |
| 137 |
\partial_t (h \theta) + \nabla \cdot ( h \theta \vec{\bf v})= 0 |
\partial_t (h \theta) + \nabla \cdot ( h \theta \vec{\bf v})= 0 |
| 138 |
$$ |
$$ |
| 139 |
Using the implicit (non-linear) free surface described above (section |
Using the implicit (non-linear) free surface described above (section |
| 140 |
\ref{sect:??}, we have: |
\ref{sect:pressure-method-linear-backward}) we have: |
| 141 |
\begin{eqnarray*} |
\begin{eqnarray*} |
| 142 |
h^{n+1} = h^{n} - \Delta_t \nabla \cdot (h^n \, \vec{\bf v}^{n+1} ) \\ |
h^{n+1} = h^{n} - \Delta_t \nabla \cdot (h^n \, \vec{\bf v}^{n+1} ) \\ |
| 143 |
\end{eqnarray*} |
\end{eqnarray*} |
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