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revision 1.6 by adcroft, Tue Sep 25 20:13:42 2001 UTC revision 1.9 by cnh, Wed Oct 24 15:21:27 2001 UTC
# Line 17  horizontal and veritical directions as s Line 17  horizontal and veritical directions as s
17    
18  The finite volume method is used to discretize the equations in  The finite volume method is used to discretize the equations in
19  space. The expression ``finite volume'' actually has two meanings; one  space. The expression ``finite volume'' actually has two meanings; one
20  is the method of cut or instecting boundaries (shaved or lopped cells  is the method of embedded or intersecting boundaries (shaved or lopped
21  in our terminology) and the other is non-linear interpolation methods  cells in our terminology) and the other is non-linear interpolation
22  that can deal with non-smooth solutions such as shocks (i.e. flux  methods that can deal with non-smooth solutions such as shocks
23  limiters for advection). Both make use of the integral form of the  (i.e. flux limiters for advection). Both make use of the integral form
24  conservation laws to which the {\it weak solution} is a solution on  of the conservation laws to which the {\it weak solution} is a
25  each finite volume of (sub-domain). The weak solution can be  solution on each finite volume of (sub-domain). The weak solution can
26  constructed outof piece-wise constant elements or be  be constructed out of piece-wise constant elements or be
27  differentiable. The differentiable equations can not be satisfied by  differentiable. The differentiable equations can not be satisfied by
28  piece-wise constant functions.  piece-wise constant functions.
29    
# Line 67  directions simultaneously. Illustration Line 67  directions simultaneously. Illustration
67  \subsection{C grid staggering of variables}  \subsection{C grid staggering of variables}
68    
69  \begin{figure}  \begin{figure}
70  \centerline{ \resizebox{!}{2in}{ \includegraphics{part2/cgrid3d.eps}} }  \begin{center}
71    \resizebox{!}{2in}{ \includegraphics{part2/cgrid3d.eps}}
72    \end{center}
73  \caption{Three dimensional staggering of velocity components. This  \caption{Three dimensional staggering of velocity components. This
74  facilitates the natural discretization of the continuity and tracer  facilitates the natural discretization of the continuity and tracer
75  equations. }  equations. }
# Line 113  grid data: ({\em model/inc/GRID.h}) Line 115  grid data: ({\em model/inc/GRID.h})
115    
116    
117  \subsection{Horizontal grid}  \subsection{Horizontal grid}
118    \label{sec:spatial_discrete_horizontal_grid}
119    
120  \begin{figure}  \begin{figure}
121  \centerline{ \begin{tabular}{cc}  \begin{center}
122    \begin{tabular}{cc}
123    \raisebox{1.5in}{a)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Ac.eps}}    \raisebox{1.5in}{a)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Ac.eps}}
124  & \raisebox{1.5in}{b)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Az.eps}}  & \raisebox{1.5in}{b)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Az.eps}}
125  \\  \\
126    \raisebox{1.5in}{c)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Au.eps}}    \raisebox{1.5in}{c)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Au.eps}}
127  & \raisebox{1.5in}{d)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Av.eps}}  & \raisebox{1.5in}{d)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Av.eps}}
128  \end{tabular} }  \end{tabular}
129    \end{center}
130  \caption{  \caption{
131  Staggering of horizontal grid descriptors (lengths and areas). The  Staggering of horizontal grid descriptors (lengths and areas). The
132  grid lines indicate the tracer cell boundaries and are the reference  grid lines indicate the tracer cell boundaries and are the reference
# Line 313  other grids, the horizontal grid descrip Line 318  other grids, the horizontal grid descrip
318  \subsection{Vertical grid}  \subsection{Vertical grid}
319    
320  \begin{figure}  \begin{figure}
321  \centerline{ \begin{tabular}{cc}  \begin{center}
322      \begin{tabular}{cc}
323    \raisebox{4in}{a)} \resizebox{!}{4in}{    \raisebox{4in}{a)} \resizebox{!}{4in}{
324    \includegraphics{part2/vgrid-cellcentered.eps}} & \raisebox{4in}{b)}    \includegraphics{part2/vgrid-cellcentered.eps}} & \raisebox{4in}{b)}
325    \resizebox{!}{4in}{ \includegraphics{part2/vgrid-accurate.eps}}    \resizebox{!}{4in}{ \includegraphics{part2/vgrid-accurate.eps}}
326  \end{tabular} }  \end{tabular}
327    \end{center}
328  \caption{Two versions of the vertical grid. a) The cell centered  \caption{Two versions of the vertical grid. a) The cell centered
329  approach where the interface depths are specified and the tracer  approach where the interface depths are specified and the tracer
330  points centered in between the interfaces. b) The interface centered  points centered in between the interfaces. b) The interface centered
# Line 382  $\Delta r_c^{-1}$: {\bf RECIP\_DRc} ({\e Line 389  $\Delta r_c^{-1}$: {\bf RECIP\_DRc} ({\e
389  \subsection{Topography: partially filled cells}  \subsection{Topography: partially filled cells}
390    
391  \begin{figure}  \begin{figure}
392  \centerline{  \begin{center}
393  \resizebox{4.5in}{!}{\includegraphics{part2/vgrid-xz.eps}}  \resizebox{4.5in}{!}{\includegraphics{part2/vgrid-xz.eps}}
394  }  \end{center}
395  \caption{  \caption{
396  A schematic of the x-r plane showing the location of the  A schematic of the x-r plane showing the location of the
397  non-dimensional fractions $h_c$ and $h_w$. The physical thickness of a  non-dimensional fractions $h_c$ and $h_w$. The physical thickness of a
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