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revision 1.13 by afe, Tue Mar 23 15:29:40 2004 UTC revision 1.19 by jmc, Wed Apr 5 01:16:27 2006 UTC
# Line 2  Line 2 
2  % $Name$  % $Name$
3    
4  \section{Spatial discretization of the dynamical equations}  \section{Spatial discretization of the dynamical equations}
5    \begin{rawhtml}
6    <!-- CMIREDIR:spatial_discretization_of_dyn_eq: -->
7    \end{rawhtml}
8    
9  Spatial discretization is carried out using the finite volume  Spatial discretization is carried out using the finite volume
10  method. This amounts to a grid-point method (namely second-order  method. This amounts to a grid-point method (namely second-order
# Line 15  horizontal and vertical directions as se Line 18  horizontal and vertical directions as se
18    
19  \subsection{The finite volume method: finite volumes versus finite difference}  \subsection{The finite volume method: finite volumes versus finite difference}
20  \begin{rawhtml}  \begin{rawhtml}
21  <!-- CMIREDIR:finite_volume -->  <!-- CMIREDIR:finite_volume: -->
22  \end{rawhtml}  \end{rawhtml}
23    
24    
# Line 147  is bordered by the lengths $\Delta x_f$ Line 150  is bordered by the lengths $\Delta x_f$
150  The model domain is decomposed into tiles and within each tile a  The model domain is decomposed into tiles and within each tile a
151  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
152  decomposition for parallelization but may be used whether parallelized  decomposition for parallelization but may be used whether parallelized
153  or not; see section \ref{sect:tiles} for more details. Although the  or not; see section \ref{sect:domain_decomposition} for more details.
154  tiles may be patched together in an unstructured manner  Although the tiles may be patched together in an unstructured manner
155  (i.e. irregular or non-tessilating pattern), the interior of tiles is  (i.e. irregular or non-tessilating pattern), the interior of tiles is
156  a structured grid of quadrilateral cells. The horizontal coordinate  a structured grid of quadrilateral cells. The horizontal coordinate
157  system is orthogonal curvilinear meaning we can not necessarily treat  system is orthogonal curvilinear meaning we can not necessarily treat
# Line 366  vertical grid descriptors are stored in Line 369  vertical grid descriptors are stored in
369    
370  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
371  approach because the tracer points are at cell centers; the cell  approach because the tracer points are at cell centers; the cell
372  centers are mid-way between the cell interfaces. An alternative, the  centers are mid-way between the cell interfaces.
373  vertex or interface centered approach, is shown in  This discretization is selected when the thickness of the
374    levels are provided ({\bf delR}, parameter file {\em data},
375    namelist {\em PARM04})
376    An alternative, the vertex or interface centered approach, is shown in
377  Fig.~\ref{fig:vgrid}b. Here, the interior interfaces are positioned  Fig.~\ref{fig:vgrid}b. Here, the interior interfaces are positioned
378  mid-way between the tracer nodes (no longer cell centers). This  mid-way between the tracer nodes (no longer cell centers). This
379  approach is formally more accurate for evaluation of hydrostatic  approach is formally more accurate for evaluation of hydrostatic
380  pressure and vertical advection but historically the cell centered  pressure and vertical advection but historically the cell centered
381  approach has been used. An alternative form of subroutine {\em  approach has been used. An alternative form of subroutine {\em
382  INI\_VERTICAL\_GRID} is used to select the interface centered approach  INI\_VERTICAL\_GRID} is used to select the interface centered approach
383  but no run time option is currently available.  This form requires to specify $Nr+1$ vertical distances {\bf delRc}
384    (parameter file {\em data}, namelist {\em PARM04}, e.g.
385    {\em verification/ideal\_2D\_oce/input/data})
386    corresponding to surface to center, $Nr-1$ center to center, and center to
387    bottom distances.
388    %but no run time option is currently available.
389    
390  \fbox{ \begin{minipage}{4.75in}  \fbox{ \begin{minipage}{4.75in}
391  {\em S/R INI\_VERTICAL\_GRID} ({\em  {\em S/R INI\_VERTICAL\_GRID} ({\em
# Line 392  $\Delta r_c^{-1}$: {\bf RECIP\_DRc} ({\e Line 403  $\Delta r_c^{-1}$: {\bf RECIP\_DRc} ({\e
403    
404    
405  \subsection{Topography: partially filled cells}  \subsection{Topography: partially filled cells}
406    \begin{rawhtml}
407    <!-- CMIREDIR:topo_partial_cells: -->
408    \end{rawhtml}
409    
410  \begin{figure}  \begin{figure}
411  \begin{center}  \begin{center}
# Line 462  $h_s^{-1}$: {\bf RECIP\_hFacS} ({\em GRI Line 476  $h_s^{-1}$: {\bf RECIP\_hFacS} ({\em GRI
476    
477    
478  \section{Continuity and horizontal pressure gradient terms}  \section{Continuity and horizontal pressure gradient terms}
479    \begin{rawhtml}
480    <!-- CMIREDIR:continuity_and_horizontal_pressure: -->
481    \end{rawhtml}
482    
483    
484  The core algorithm is based on the ``C grid'' discretization of the  The core algorithm is based on the ``C grid'' discretization of the
485  continuity equation which can be summarized as:  continuity equation which can be summarized as:
# Line 500  addition of volume due to excess precipi Line 518  addition of volume due to excess precipi
518  evaporation and only enters the top-level of the {\em ocean} model.  evaporation and only enters the top-level of the {\em ocean} model.
519    
520  \section{Hydrostatic balance}  \section{Hydrostatic balance}
521    \begin{rawhtml}
522    <!-- CMIREDIR:hydrostatic_balance: -->
523    \end{rawhtml}
524    
525  The vertical momentum equation has the hydrostatic or  The vertical momentum equation has the hydrostatic or
526  quasi-hydrostatic balance on the right hand side. This discretization  quasi-hydrostatic balance on the right hand side. This discretization
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