--- manual/s_algorithm/text/spatial-discrete.tex 2004/10/13 18:50:54 1.16 +++ manual/s_algorithm/text/spatial-discrete.tex 2006/06/27 19:10:32 1.20 @@ -1,7 +1,10 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/spatial-discrete.tex,v 1.16 2004/10/13 18:50:54 jmc Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/spatial-discrete.tex,v 1.20 2006/06/27 19:10:32 jmc Exp $ % $Name: $ \section{Spatial discretization of the dynamical equations} +\begin{rawhtml} + +\end{rawhtml} Spatial discretization is carried out using the finite volume method. This amounts to a grid-point method (namely second-order @@ -10,8 +13,6 @@ representation of the position of the boundary. We treat the horizontal and vertical directions as separable and differently. -\input{part2/notation} - \subsection{The finite volume method: finite volumes versus finite difference} \begin{rawhtml} @@ -147,8 +148,8 @@ The model domain is decomposed into tiles and within each tile a quasi-regular grid is used. A tile is the basic unit of domain decomposition for parallelization but may be used whether parallelized -or not; see section \ref{sect:tiles} for more details. Although the -tiles may be patched together in an unstructured manner +or not; see section \ref{sect:domain_decomposition} for more details. +Although the tiles may be patched together in an unstructured manner (i.e. irregular or non-tessilating pattern), the interior of tiles is a structured grid of quadrilateral cells. The horizontal coordinate system is orthogonal curvilinear meaning we can not necessarily treat @@ -367,7 +368,7 @@ The above grid (Fig.~\ref{fig:vgrid}a) is known as the cell centered approach because the tracer points are at cell centers; the cell centers are mid-way between the cell interfaces. -This discretisation is selected when the thickness of the +This discretization is selected when the thickness of the levels are provided ({\bf delR}, parameter file {\em data}, namelist {\em PARM04}) An alternative, the vertex or interface centered approach, is shown in @@ -473,6 +474,10 @@ \section{Continuity and horizontal pressure gradient terms} +\begin{rawhtml} + +\end{rawhtml} + The core algorithm is based on the ``C grid'' discretization of the continuity equation which can be summarized as: @@ -511,6 +516,9 @@ evaporation and only enters the top-level of the {\em ocean} model. \section{Hydrostatic balance} +\begin{rawhtml} + +\end{rawhtml} The vertical momentum equation has the hydrostatic or quasi-hydrostatic balance on the right hand side. This discretization