--- manual/s_algorithm/text/tracer.tex	2004/10/16 03:40:13	1.18
+++ manual/s_algorithm/text/tracer.tex	2008/01/17 17:42:11	1.24
@@ -1,4 +1,4 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/tracer.tex,v 1.18 2004/10/16 03:40:13 edhill Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/tracer.tex,v 1.24 2008/01/17 17:42:11 cnh Exp $
 % $Name:  $
 
 \section{Tracer equations}
@@ -359,6 +359,7 @@
 
 
 \section{Non-linear advection schemes}
+\label{sect:non-linear_advection_schemes}
 \begin{rawhtml}
 <!-- CMIREDIR:non-linear_advection_schemes: -->
 \end{rawhtml}
@@ -627,10 +628,10 @@
 \tau^{n+1/3} & = & \tau^{n}
 - \Delta t \left( \frac{1}{\Delta x} \delta_i F^x(\tau^{n})
            + \tau^{n} \frac{1}{\Delta x} \delta_i u \right) \\
-\tau^{n+2/3} & = & \tau^{n}
+\tau^{n+2/3} & = & \tau^{n+1/3}
 - \Delta t \left( \frac{1}{\Delta y} \delta_j F^y(\tau^{n+1/3})
            + \tau^{n} \frac{1}{\Delta y} \delta_i v \right) \\
-\tau^{n+3/3} & = & \tau^{n}
+\tau^{n+3/3} & = & \tau^{n+2/3}
 - \Delta t \left( \frac{1}{\Delta r} \delta_k F^x(\tau^{n+2/3})
            + \tau^{n} \frac{1}{\Delta r} \delta_i w \right)
 \end{eqnarray}
@@ -664,8 +665,15 @@
 
 \end{minipage} }
 
+\begin{figure}
+\resizebox{3.5in}{!}{\includegraphics{part2/multiDim_CS.eps}}
+\caption{Muti-dimensional advection time-stepping with Cubed-Sphere topology
+\label{fig:advect-multidim_cs}
+}
+\end{figure}
 
 \section{Comparison of advection schemes}
+\label{sect:tracer_advection_schemes}
 \begin{rawhtml}
 <!-- CMIREDIR:comparison_of_advection_schemes: -->
 \end{rawhtml}
@@ -677,15 +685,18 @@
    Advection Scheme & code & use  & use Multi- & Stencil & comments \\
                     &      & A.B. & dimension & (1 dim) & \\
    \hline \hline
+   $1^{rst}$order upwind  & 1 &  No & Yes & 3 pts & linear/$\tau$, non-linear/v\\
+   \hline
    centered $2^{nd}$order & 2 &  Yes & No & 3 pts & linear \\
    \hline
-   $3^{rd}$order upwind   & 3 &  Yes & No & 5 pts & linear/tracer\\
+   $3^{rd}$order upwind   & 3 &  Yes & No & 5 pts & linear/$\tau$\\
    \hline
    centered $4^{th}$order & 4 &  Yes & No & 5 pts & linear \\
    \hline \hline
-%  Lax-Wendroff       & 10 &  No & Yes & 3 pts & linear/tracer, non-linear/flow\\
-%  \hline
-   $3^{rd}$order DST & 30 &  No & Yes & 5 pts & linear/tracer, non-linear/flow\\
+   $2^{nd}$order DST (Lax-Wendroff)  & 20 &
+                         No & Yes & 3 pts & linear/$\tau$, non-linear/v\\
+   \hline
+   $3^{rd}$order DST & 30 &  No & Yes & 5 pts & linear/$\tau$, non-linear/v\\
    \hline \hline
    $2^{nd}$order Flux Limiters & 77 &  No & Yes & 5 pts & non-linear \\
    \hline
@@ -695,7 +706,7 @@
  \caption{Summary of the different advection schemes available in MITgcm.
           ``A.B.'' stands for Adams-Bashforth and ``DST'' for direct space time.
           The code corresponds to the number used to select the corresponding
-          advection scheme in the parameter file (e.g., {\em tempAdvScheme=3} in
+          advection scheme in the parameter file (e.g., {\bf tempAdvScheme}=3 in
           file {\em data} selects the $3^{rd}$ order upwind advection scheme 
           for temperature).
    }