--- manual/s_algorithm/text/tracer.tex 2004/03/23 15:29:40 1.14 +++ manual/s_algorithm/text/tracer.tex 2004/10/14 19:53:04 1.17 @@ -1,4 +1,4 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/tracer.tex,v 1.14 2004/03/23 15:29:40 afe Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/tracer.tex,v 1.17 2004/10/14 19:53:04 jmc Exp $ % $Name: $ \section{Tracer equations} @@ -125,7 +125,7 @@ \section{Linear advection schemes} \label{sect:tracer-advection} \begin{rawhtml} - + \end{rawhtml} \begin{figure} @@ -353,6 +353,9 @@ \section{Non-linear advection schemes} +\begin{rawhtml} + +\end{rawhtml} Non-linear advection schemes invoke non-linear interpolation and are widely used in computational fluid dynamics (non-linear does not refer @@ -658,6 +661,39 @@ \section{Comparison of advection schemes} +\begin{table}[htb] +\centering + \begin{tabular}[htb]{|l|c|c|c|c|l|} + \hline + Advection Scheme & code & use & use Multi- & Stencil & comments \\ + & & A.B. & dimension & (1 dim) & \\ + \hline \hline + centered $2^{nd}$order & 2 & Yes & No & 3 pts & linear \\ + \hline + $3^{rd}$order upwind & 3 & Yes & No & 5 pts & linear/tracer\\ + \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\\ + \hline \hline + $2^{nd}$order Flux Limiters & 77 & No & Yes & 5 pts & non-linear \\ + \hline + $3^{nd}$order DST Flux limiter & 33 & No & Yes & 5 pts & non-linear \\ + \hline + \end{tabular} + \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 + file {\em data} selects the $3^{rd}$ order upwind advection scheme + for temperature). + } + \label{tab:advectionShemes_summary} +\end{table} + + Figs.~\ref{fig:advect-2d-lo-diag}, \ref{fig:advect-2d-mid-diag} and \ref{fig:advect-2d-hi-diag} show solutions to a simple diagonal advection problem using a selection of schemes for low, moderate and