--- manual/s_algorithm/text/spatial-discrete.tex 2006/04/05 01:16:27 1.19 +++ manual/s_algorithm/text/spatial-discrete.tex 2010/08/27 13:08:18 1.23 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/spatial-discrete.tex,v 1.19 2006/04/05 01:16:27 jmc Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/spatial-discrete.tex,v 1.23 2010/08/27 13:08:18 jmc Exp $ % $Name: $ \section{Spatial discretization of the dynamical equations} @@ -13,8 +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} @@ -76,7 +74,7 @@ \begin{figure} \begin{center} -\resizebox{!}{2in}{ \includegraphics{part2/cgrid3d.eps}} +\resizebox{!}{2in}{ \includegraphics{s_algorithm/figs/cgrid3d.eps}} \end{center} \caption{Three dimensional staggering of velocity components. This facilitates the natural discretization of the continuity and tracer @@ -128,11 +126,11 @@ \begin{figure} \begin{center} \begin{tabular}{cc} - \raisebox{1.5in}{a)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Ac.eps}} -& \raisebox{1.5in}{b)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Az.eps}} + \raisebox{1.5in}{a)}\resizebox{!}{2in}{ \includegraphics{s_algorithm/figs/hgrid-Ac.eps}} +& \raisebox{1.5in}{b)}\resizebox{!}{2in}{ \includegraphics{s_algorithm/figs/hgrid-Az.eps}} \\ - \raisebox{1.5in}{c)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Au.eps}} -& \raisebox{1.5in}{d)}\resizebox{!}{2in}{ \includegraphics{part2/hgrid-Av.eps}} + \raisebox{1.5in}{c)}\resizebox{!}{2in}{ \includegraphics{s_algorithm/figs/hgrid-Au.eps}} +& \raisebox{1.5in}{d)}\resizebox{!}{2in}{ \includegraphics{s_algorithm/figs/hgrid-Av.eps}} \end{tabular} \end{center} \caption{ @@ -141,8 +139,8 @@ grid for all panels. a) The area of a tracer cell, $A_c$, is bordered by the lengths $\Delta x_g$ and $\Delta y_g$. b) The area of a vorticity cell, $A_\zeta$, is bordered by the lengths $\Delta x_c$ and -$\Delta y_c$. c) The area of a u cell, $A_c$, is bordered by the -lengths $\Delta x_v$ and $\Delta y_f$. d) The area of a v cell, $A_c$, +$\Delta y_c$. c) The area of a u cell, $A_w$, is bordered by the +lengths $\Delta x_v$ and $\Delta y_f$. d) The area of a v cell, $A_s$, is bordered by the lengths $\Delta x_f$ and $\Delta y_u$.} \label{fig:hgrid} \end{figure} @@ -188,7 +186,7 @@ Fig.~\ref{fig:hgrid}b shows the vorticity cell. The length of the southern edge, $\Delta x_c$, western edge, $\Delta y_c$ and surface area, $A_\zeta$, presented in the vertical are stored in arrays {\bf -DXg}, {\bf DYg} and {\bf rAz}. +DXc}, {\bf DYc} and {\bf rAz}. \marginpar{$A_\zeta$: {\bf rAz}} \marginpar{$\Delta x_c$: {\bf DXc}} \marginpar{$\Delta y_c$: {\bf DYc}} @@ -329,8 +327,8 @@ \begin{center} \begin{tabular}{cc} \raisebox{4in}{a)} \resizebox{!}{4in}{ - \includegraphics{part2/vgrid-cellcentered.eps}} & \raisebox{4in}{b)} - \resizebox{!}{4in}{ \includegraphics{part2/vgrid-accurate.eps}} + \includegraphics{s_algorithm/figs/vgrid-cellcentered.eps}} & \raisebox{4in}{b)} + \resizebox{!}{4in}{ \includegraphics{s_algorithm/figs/vgrid-accurate.eps}} \end{tabular} \end{center} \caption{Two versions of the vertical grid. a) The cell centered @@ -409,7 +407,7 @@ \begin{figure} \begin{center} -\resizebox{4.5in}{!}{\includegraphics{part2/vgrid-xz.eps}} +\resizebox{4.5in}{!}{\includegraphics{s_algorithm/figs/vgrid-xz.eps}} \end{center} \caption{ A schematic of the x-r plane showing the location of the