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revision 1.19 by jmc, Wed Apr 5 01:16:27 2006 UTC revision 1.23 by jmc, Fri Aug 27 13:08:18 2010 UTC
# Line 13  boundaries to intersect a regular grid a Line 13  boundaries to intersect a regular grid a
13  representation of the position of the boundary. We treat the  representation of the position of the boundary. We treat the
14  horizontal and vertical directions as separable and differently.  horizontal and vertical directions as separable and differently.
15    
 \input{part2/notation}  
   
16    
17  \subsection{The finite volume method: finite volumes versus finite difference}  \subsection{The finite volume method: finite volumes versus finite difference}
18  \begin{rawhtml}  \begin{rawhtml}
# Line 76  directions simultaneously. Illustration Line 74  directions simultaneously. Illustration
74    
75  \begin{figure}  \begin{figure}
76  \begin{center}  \begin{center}
77  \resizebox{!}{2in}{ \includegraphics{part2/cgrid3d.eps}}  \resizebox{!}{2in}{ \includegraphics{s_algorithm/figs/cgrid3d.eps}}
78  \end{center}  \end{center}
79  \caption{Three dimensional staggering of velocity components. This  \caption{Three dimensional staggering of velocity components. This
80  facilitates the natural discretization of the continuity and tracer  facilitates the natural discretization of the continuity and tracer
# Line 128  grid data: ({\em model/inc/GRID.h}) Line 126  grid data: ({\em model/inc/GRID.h})
126  \begin{figure}  \begin{figure}
127  \begin{center}  \begin{center}
128  \begin{tabular}{cc}  \begin{tabular}{cc}
129    \raisebox{1.5in}{a)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Ac.eps}}    \raisebox{1.5in}{a)}\resizebox{!}{2in}{ \includegraphics{s_algorithm/figs/hgrid-Ac.eps}}
130  & \raisebox{1.5in}{b)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Az.eps}}  & \raisebox{1.5in}{b)}\resizebox{!}{2in}{ \includegraphics{s_algorithm/figs/hgrid-Az.eps}}
131  \\  \\
132    \raisebox{1.5in}{c)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Au.eps}}    \raisebox{1.5in}{c)}\resizebox{!}{2in}{ \includegraphics{s_algorithm/figs/hgrid-Au.eps}}
133  & \raisebox{1.5in}{d)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Av.eps}}  & \raisebox{1.5in}{d)}\resizebox{!}{2in}{ \includegraphics{s_algorithm/figs/hgrid-Av.eps}}
134  \end{tabular}  \end{tabular}
135  \end{center}  \end{center}
136  \caption{  \caption{
# Line 141  grid lines indicate the tracer cell boun Line 139  grid lines indicate the tracer cell boun
139  grid for all panels. a) The area of a tracer cell, $A_c$, is bordered  grid for all panels. a) The area of a tracer cell, $A_c$, is bordered
140  by the lengths $\Delta x_g$ and $\Delta y_g$. b) The area of a  by the lengths $\Delta x_g$ and $\Delta y_g$. b) The area of a
141  vorticity cell, $A_\zeta$, is bordered by the lengths $\Delta x_c$ and  vorticity cell, $A_\zeta$, is bordered by the lengths $\Delta x_c$ and
142  $\Delta y_c$. c) The area of a u cell, $A_c$, is bordered by the  $\Delta y_c$. c) The area of a u cell, $A_w$, is bordered by the
143  lengths $\Delta x_v$ and $\Delta y_f$. d) The area of a v cell, $A_c$,  lengths $\Delta x_v$ and $\Delta y_f$. d) The area of a v cell, $A_s$,
144  is bordered by the lengths $\Delta x_f$ and $\Delta y_u$.}  is bordered by the lengths $\Delta x_f$ and $\Delta y_u$.}
145  \label{fig:hgrid}  \label{fig:hgrid}
146  \end{figure}  \end{figure}
# Line 188  rAc(i,j)} and {\bf DYg(i,j)} positioned Line 186  rAc(i,j)} and {\bf DYg(i,j)} positioned
186  Fig.~\ref{fig:hgrid}b shows the vorticity cell. The length of the  Fig.~\ref{fig:hgrid}b shows the vorticity cell. The length of the
187  southern edge, $\Delta x_c$, western edge, $\Delta y_c$ and surface  southern edge, $\Delta x_c$, western edge, $\Delta y_c$ and surface
188  area, $A_\zeta$, presented in the vertical are stored in arrays {\bf  area, $A_\zeta$, presented in the vertical are stored in arrays {\bf
189  DXg}, {\bf DYg} and {\bf rAz}.  DXc}, {\bf DYc} and {\bf rAz}.
190  \marginpar{$A_\zeta$: {\bf rAz}}  \marginpar{$A_\zeta$: {\bf rAz}}
191  \marginpar{$\Delta x_c$: {\bf DXc}}  \marginpar{$\Delta x_c$: {\bf DXc}}
192  \marginpar{$\Delta y_c$: {\bf DYc}}  \marginpar{$\Delta y_c$: {\bf DYc}}
# Line 329  other grids, the horizontal grid descrip Line 327  other grids, the horizontal grid descrip
327  \begin{center}  \begin{center}
328    \begin{tabular}{cc}    \begin{tabular}{cc}
329    \raisebox{4in}{a)} \resizebox{!}{4in}{    \raisebox{4in}{a)} \resizebox{!}{4in}{
330    \includegraphics{part2/vgrid-cellcentered.eps}} & \raisebox{4in}{b)}    \includegraphics{s_algorithm/figs/vgrid-cellcentered.eps}} & \raisebox{4in}{b)}
331    \resizebox{!}{4in}{ \includegraphics{part2/vgrid-accurate.eps}}    \resizebox{!}{4in}{ \includegraphics{s_algorithm/figs/vgrid-accurate.eps}}
332  \end{tabular}  \end{tabular}
333  \end{center}  \end{center}
334  \caption{Two versions of the vertical grid. a) The cell centered  \caption{Two versions of the vertical grid. a) The cell centered
# Line 409  $\Delta r_c^{-1}$: {\bf RECIP\_DRc} ({\e Line 407  $\Delta r_c^{-1}$: {\bf RECIP\_DRc} ({\e
407    
408  \begin{figure}  \begin{figure}
409  \begin{center}  \begin{center}
410  \resizebox{4.5in}{!}{\includegraphics{part2/vgrid-xz.eps}}  \resizebox{4.5in}{!}{\includegraphics{s_algorithm/figs/vgrid-xz.eps}}
411  \end{center}  \end{center}
412  \caption{  \caption{
413  A schematic of the x-r plane showing the location of the  A schematic of the x-r plane showing the location of the
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