--- manual/s_algorithm/text/tracer.tex 2002/05/06 19:19:31 1.13 +++ manual/s_algorithm/text/tracer.tex 2004/10/17 04:14:21 1.19 @@ -1,8 +1,11 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/tracer.tex,v 1.13 2002/05/06 19:19:31 adcroft Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/tracer.tex,v 1.19 2004/10/17 04:14:21 jmc Exp $ % $Name: $ \section{Tracer equations} \label{sect:tracer_equations} +\begin{rawhtml} + +\end{rawhtml} The basic discretization used for the tracer equations is the second order piece-wise constant finite volume form of the forced @@ -16,6 +19,9 @@ \subsection{Time-stepping of tracers: ABII} \label{sect:tracer_equations_abII} +\begin{rawhtml} + +\end{rawhtml} The default advection scheme is the centered second order method which requires a second order or quasi-second order time-stepping scheme to @@ -124,6 +130,9 @@ \section{Linear advection schemes} \label{sect:tracer-advection} +\begin{rawhtml} + +\end{rawhtml} \begin{figure} \resizebox{5.5in}{!}{\includegraphics{part2/advect-1d-lo.eps}} @@ -350,6 +359,9 @@ \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 @@ -654,6 +666,42 @@ \section{Comparison of advection schemes} +\begin{rawhtml} + +\end{rawhtml} + +\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/$\tau$\\ + \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/$\tau$, non-linear/v\\ + \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., {\bf 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