| 4 |
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| 5 |
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| 6 |
\subsection{Non-linear free surface} |
\subsection{Non-linear free surface} |
| 7 |
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\label{sect:nonlinear-freesurface} |
| 8 |
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| 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. |
| 64 |
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| 65 |
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| 66 |
The continuous form of the model equations remains unchanged, except |
The continuous form of the model equations remains unchanged, except |
| 67 |
for the 2D continuity equation (\ref{eq-tCsC-eta}) which is now |
for the 2D continuity equation (\ref{eq:discrete-time-backward-free-surface}) which is now |
| 68 |
integrated from $R_{fixed}(x,y)$ up to $r_{surf}=R_o+\eta$ : |
integrated from $R_{fixed}(x,y)$ up to $r_{surf}=R_o+\eta$ : |
| 69 |
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| 70 |
\begin{displaymath} |
\begin{displaymath} |
| 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 |
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$$ |
$$ |
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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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