/[MITgcm]/manual/s_algorithm/text/tracer.tex
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revision 1.11 by adcroft, Tue Nov 13 19:01:42 2001 UTC revision 1.15 by afe, Tue Mar 23 16:47:04 2004 UTC
# Line 2  Line 2 
2  % $Name$  % $Name$
3    
4  \section{Tracer equations}  \section{Tracer equations}
5  \label{sec:tracer_equations}  \label{sect:tracer_equations}
6    
7  The basic discretization used for the tracer equations is the second  The basic discretization used for the tracer equations is the second
8  order piece-wise constant finite volume form of the forced  order piece-wise constant finite volume form of the forced
# Line 15  part of the tracer equations and the var Line 15  part of the tracer equations and the var
15  described here.  described here.
16    
17  \subsection{Time-stepping of tracers: ABII}  \subsection{Time-stepping of tracers: ABII}
18  \label{sec:tracer_equations_abII}  \label{sect:tracer_equations_abII}
19    
20  The default advection scheme is the centered second order method which  The default advection scheme is the centered second order method which
21  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 123  the forward method. Line 123  the forward method.
123    
124    
125  \section{Linear advection schemes}  \section{Linear advection schemes}
126    \label{sect:tracer-advection}
127    \begin{rawhtml}
128    <!-- CMIREDIR:linear_advection_schemes: -->
129    \end{rawhtml}
130    
131  \begin{figure}  \begin{figure}
132  \resizebox{5.5in}{!}{\includegraphics{part2/advect-1d-lo.eps}}  \resizebox{5.5in}{!}{\includegraphics{part2/advect-1d-lo.eps}}
# Line 449  to centered second order advection in th Line 453  to centered second order advection in th
453    
454  The DST3 method described above must be used in a forward-in-time  The DST3 method described above must be used in a forward-in-time
455  manner and is stable for $0 \le |c| \le 1$. Although the scheme  manner and is stable for $0 \le |c| \le 1$. Although the scheme
456  appears to be forward-in-time, it is in fact second order in time and  appears to be forward-in-time, it is in fact third order in time and
457  the accuracy increases with the Courant number! For low Courant  the accuracy increases with the Courant number! For low Courant
458  number, DST3 produces very similar results (indistinguishable in  number, DST3 produces very similar results (indistinguishable in
459  Fig.~\ref{fig:advect-1d-lo}) to the linear third order method but for  Fig.~\ref{fig:advect-1d-lo}) to the linear third order method but for
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