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\section{Spatial discretization of the dynamical equations} |
\section{Spatial discretization of the dynamical equations} |
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<!-- CMIREDIR:spatial_discretization_of_dyn_eq: --> |
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Spatial discretization is carried out using the finite volume |
Spatial discretization is carried out using the finite volume |
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method. This amounts to a grid-point method (namely second-order |
method. This amounts to a grid-point method (namely second-order |
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The model domain is decomposed into tiles and within each tile a |
The model domain is decomposed into tiles and within each tile a |
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quasi-regular grid is used. A tile is the basic unit of domain |
quasi-regular grid is used. A tile is the basic unit of domain |
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decomposition for parallelization but may be used whether parallelized |
decomposition for parallelization but may be used whether parallelized |
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or not; see section \ref{sect:tiles} for more details. Although the |
or not; see section \ref{sect:domain_decomposition} for more details. |
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tiles may be patched together in an unstructured manner |
Although the tiles may be patched together in an unstructured manner |
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(i.e. irregular or non-tessilating pattern), the interior of tiles is |
(i.e. irregular or non-tessilating pattern), the interior of tiles is |
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a structured grid of quadrilateral cells. The horizontal coordinate |
a structured grid of quadrilateral cells. The horizontal coordinate |
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system is orthogonal curvilinear meaning we can not necessarily treat |
system is orthogonal curvilinear meaning we can not necessarily treat |
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The above grid (Fig.~\ref{fig:vgrid}a) is known as the cell centered |
The above grid (Fig.~\ref{fig:vgrid}a) is known as the cell centered |
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approach because the tracer points are at cell centers; the cell |
approach because the tracer points are at cell centers; the cell |
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centers are mid-way between the cell interfaces. |
centers are mid-way between the cell interfaces. |
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This discretisation is selected when the thickness of the |
This discretization is selected when the thickness of the |
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levels are provided ({\bf delR}, parameter file {\em data}, |
levels are provided ({\bf delR}, parameter file {\em data}, |
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namelist {\em PARM04}) |
namelist {\em PARM04}) |
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An alternative, the vertex or interface centered approach, is shown in |
An alternative, the vertex or interface centered approach, is shown in |
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\section{Continuity and horizontal pressure gradient terms} |
\section{Continuity and horizontal pressure gradient terms} |
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<!-- CMIREDIR:continuity_and_horizontal_pressure: --> |
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The core algorithm is based on the ``C grid'' discretization of the |
The core algorithm is based on the ``C grid'' discretization of the |
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continuity equation which can be summarized as: |
continuity equation which can be summarized as: |
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evaporation and only enters the top-level of the {\em ocean} model. |
evaporation and only enters the top-level of the {\em ocean} model. |
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\section{Hydrostatic balance} |
\section{Hydrostatic balance} |
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<!-- CMIREDIR:hydrostatic_balance: --> |
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The vertical momentum equation has the hydrostatic or |
The vertical momentum equation has the hydrostatic or |
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quasi-hydrostatic balance on the right hand side. This discretization |
quasi-hydrostatic balance on the right hand side. This discretization |
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