/[MITgcm]/manual/s_algorithm/text/tracer.tex
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revision 1.17 by jmc, Thu Oct 14 19:53:04 2004 UTC revision 1.20 by jmc, Thu Jul 7 21:36:34 2005 UTC
# Line 3  Line 3 
3    
4  \section{Tracer equations}  \section{Tracer equations}
5  \label{sect:tracer_equations}  \label{sect:tracer_equations}
6    \begin{rawhtml}
7    <!-- CMIREDIR:tracer_equations: -->
8    \end{rawhtml}
9    
10  The basic discretization used for the tracer equations is the second  The basic discretization used for the tracer equations is the second
11  order piece-wise constant finite volume form of the forced  order piece-wise constant finite volume form of the forced
# Line 16  described here. Line 19  described here.
19    
20  \subsection{Time-stepping of tracers: ABII}  \subsection{Time-stepping of tracers: ABII}
21  \label{sect:tracer_equations_abII}  \label{sect:tracer_equations_abII}
22    \begin{rawhtml}
23    <!-- CMIREDIR:tracer_equations_abII: -->
24    \end{rawhtml}
25    
26  The default advection scheme is the centered second order method which  The default advection scheme is the centered second order method which
27  requires a second order or quasi-second order time-stepping scheme to  requires a second order or quasi-second order time-stepping scheme to
# Line 660  $W$: {\bf rTrans} (local) Line 666  $W$: {\bf rTrans} (local)
666    
667    
668  \section{Comparison of advection schemes}  \section{Comparison of advection schemes}
669    \label{sect:tracer_advection_schemes}
670    \begin{rawhtml}
671    <!-- CMIREDIR:comparison_of_advection_schemes: -->
672    \end{rawhtml}
673    
674  \begin{table}[htb]  \begin{table}[htb]
675  \centering  \centering
# Line 670  $W$: {\bf rTrans} (local) Line 680  $W$: {\bf rTrans} (local)
680     \hline \hline     \hline \hline
681     centered $2^{nd}$order & 2 &  Yes & No & 3 pts & linear \\     centered $2^{nd}$order & 2 &  Yes & No & 3 pts & linear \\
682     \hline     \hline
683     $3^{rd}$order upwind   & 3 &  Yes & No & 5 pts & linear/tracer\\     $3^{rd}$order upwind   & 3 &  Yes & No & 5 pts & linear/$\tau$\\
684     \hline     \hline
685     centered $4^{th}$order & 4 &  Yes & No & 5 pts & linear \\     centered $4^{th}$order & 4 &  Yes & No & 5 pts & linear \\
686     \hline \hline     \hline \hline
687  %  Lax-Wendroff       & 10 &  No & Yes & 3 pts & linear/tracer, non-linear/flow\\  %  Lax-Wendroff       & 10 &  No & Yes & 3 pts & linear/tracer, non-linear/flow\\
688  %  \hline  %  \hline
689     $3^{rd}$order DST & 30 &  No & Yes & 5 pts & linear/tracer, non-linear/flow\\     $3^{rd}$order DST & 30 &  No & Yes & 5 pts & linear/$\tau$, non-linear/v\\
690     \hline \hline     \hline \hline
691     $2^{nd}$order Flux Limiters & 77 &  No & Yes & 5 pts & non-linear \\     $2^{nd}$order Flux Limiters & 77 &  No & Yes & 5 pts & non-linear \\
692     \hline     \hline
# Line 686  $W$: {\bf rTrans} (local) Line 696  $W$: {\bf rTrans} (local)
696   \caption{Summary of the different advection schemes available in MITgcm.   \caption{Summary of the different advection schemes available in MITgcm.
697            ``A.B.'' stands for Adams-Bashforth and ``DST'' for direct space time.            ``A.B.'' stands for Adams-Bashforth and ``DST'' for direct space time.
698            The code corresponds to the number used to select the corresponding            The code corresponds to the number used to select the corresponding
699            advection scheme in the parameter file (e.g., {\em tempAdvScheme=3} in            advection scheme in the parameter file (e.g., {\bf tempAdvScheme}=3 in
700            file {\em data} selects the $3^{rd}$ order upwind advection scheme            file {\em data} selects the $3^{rd}$ order upwind advection scheme
701            for temperature).            for temperature).
702     }     }
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