| 57 |
interior of a fluid. Differences arise at boundaries where a boundary |
interior of a fluid. Differences arise at boundaries where a boundary |
| 58 |
is not positioned on a regular or smoothly varying grid. This method |
is not positioned on a regular or smoothly varying grid. This method |
| 59 |
is used to represent the topography using lopped cell, see |
is used to represent the topography using lopped cell, see |
| 60 |
\cite{Adcroft98}. Subtle difference also appear in more than one |
\cite{adcroft:97}. Subtle difference also appear in more than one |
| 61 |
dimension away from boundaries. This happens because the each |
dimension away from boundaries. This happens because the each |
| 62 |
direction is discretized independently in the finite difference method |
direction is discretized independently in the finite difference method |
| 63 |
while the integrating over finite volume implicitly treats all |
while the integrating over finite volume implicitly treats all |
| 64 |
directions simultaneously. Illustration of this is given in |
directions simultaneously. Illustration of this is given in |
| 65 |
\cite{Adcroft02}. |
\cite{ac:02}. |
| 66 |
|
|
| 67 |
\subsection{C grid staggering of variables} |
\subsection{C grid staggering of variables} |
| 68 |
|
|
| 79 |
The basic algorithm employed for stepping forward the momentum |
The basic algorithm employed for stepping forward the momentum |
| 80 |
equations is based on retaining non-divergence of the flow at all |
equations is based on retaining non-divergence of the flow at all |
| 81 |
times. This is most naturally done if the components of flow are |
times. This is most naturally done if the components of flow are |
| 82 |
staggered in space in the form of an Arakawa C grid \cite{Arakawa70}. |
staggered in space in the form of an Arakawa C grid \cite{arakawa:77}. |
| 83 |
|
|
| 84 |
Fig. \ref{fig:cgrid3d} shows the components of flow ($u$,$v$,$w$) |
Fig. \ref{fig:cgrid3d} shows the components of flow ($u$,$v$,$w$) |
| 85 |
staggered in space such that the zonal component falls on the |
staggered in space such that the zonal component falls on the |
| 400 |
\label{fig:hfacs} |
\label{fig:hfacs} |
| 401 |
\end{figure} |
\end{figure} |
| 402 |
|
|
| 403 |
\cite{Adcroft97} presented two alternatives to the step-wise finite |
\cite{adcroft:97} presented two alternatives to the step-wise finite |
| 404 |
difference representation of topography. The method is known to the |
difference representation of topography. The method is known to the |
| 405 |
engineering community as {\em intersecting boundary method}. It |
engineering community as {\em intersecting boundary method}. It |
| 406 |
involves allowing the boundary to intersect a grid of cells thereby |
involves allowing the boundary to intersect a grid of cells thereby |
| 524 |
The difference in approach between ocean and atmosphere occurs because |
The difference in approach between ocean and atmosphere occurs because |
| 525 |
of the direct use of the ideal gas equation in forming the potential |
of the direct use of the ideal gas equation in forming the potential |
| 526 |
energy conversion term $\alpha \omega$. The form of these conversion |
energy conversion term $\alpha \omega$. The form of these conversion |
| 527 |
terms is discussed at length in \cite{Adcroft01}. |
terms is discussed at length in \cite{adcroft:02}. |
| 528 |
|
|
| 529 |
Because of the different representation of hydrostatic balance between |
Because of the different representation of hydrostatic balance between |
| 530 |
ocean and atmosphere there is no elegant way to represent both systems |
ocean and atmosphere there is no elegant way to represent both systems |
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