/[MITgcm]/manual/s_algorithm/text/tracer.tex
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revision 1.23 by jmc, Tue Jan 15 23:52:12 2008 UTC revision 1.26 by jmc, Mon Aug 30 23:09:19 2010 UTC
# Line 2  Line 2 
2  % $Name$  % $Name$
3    
4  \section{Tracer equations}  \section{Tracer equations}
5  \label{sect:tracer_equations}  \label{sec:tracer_equations}
6  \begin{rawhtml}  \begin{rawhtml}
7  <!-- CMIREDIR:tracer_equations: -->  <!-- CMIREDIR:tracer_equations: -->
8  \end{rawhtml}  \end{rawhtml}
# Line 18  part of the tracer equations and the var Line 18  part of the tracer equations and the var
18  described here.  described here.
19    
20  \subsection{Time-stepping of tracers: ABII}  \subsection{Time-stepping of tracers: ABII}
21  \label{sect:tracer_equations_abII}  \label{sec:tracer_equations_abII}
22  \begin{rawhtml}  \begin{rawhtml}
23  <!-- CMIREDIR:tracer_equations_abII: -->  <!-- CMIREDIR:tracer_equations_abII: -->
24  \end{rawhtml}  \end{rawhtml}
# Line 129  the forward method. Line 129  the forward method.
129    
130    
131  \section{Linear advection schemes}  \section{Linear advection schemes}
132  \label{sect:tracer-advection}  \label{sec:tracer-advection}
133  \begin{rawhtml}  \begin{rawhtml}
134  <!-- CMIREDIR:linear_advection_schemes: -->  <!-- CMIREDIR:linear_advection_schemes: -->
135  \end{rawhtml}  \end{rawhtml}
136    
137  \begin{figure}  \begin{figure}
138  \resizebox{5.5in}{!}{\includegraphics{part2/advect-1d-lo.eps}}  \resizebox{5.5in}{!}{\includegraphics{s_algorithm/figs/advect-1d-lo.eps}}
139  \caption{  \caption{
140  Comparison of 1-D advection schemes. Courant number is 0.05 with 60  Comparison of 1-D advection schemes. Courant number is 0.05 with 60
141  points and solutions are shown for T=1 (one complete period).  points and solutions are shown for T=1 (one complete period).
# Line 153  $\mu=c/(1-c)$. Line 153  $\mu=c/(1-c)$.
153  \end{figure}  \end{figure}
154    
155  \begin{figure}  \begin{figure}
156  \resizebox{5.5in}{!}{\includegraphics{part2/advect-1d-hi.eps}}  \resizebox{5.5in}{!}{\includegraphics{s_algorithm/figs/advect-1d-hi.eps}}
157  \caption{  \caption{
158  Comparison of 1-D advection schemes. Courant number is 0.89 with 60  Comparison of 1-D advection schemes. Courant number is 0.89 with 60
159  points and solutions are shown for T=1 (one complete period).  points and solutions are shown for T=1 (one complete period).
# Line 359  if the limiter is set to zero. Line 359  if the limiter is set to zero.
359    
360    
361  \section{Non-linear advection schemes}  \section{Non-linear advection schemes}
362    \label{sec:non-linear_advection_schemes}
363  \begin{rawhtml}  \begin{rawhtml}
364  <!-- CMIREDIR:non-linear_advection_schemes: -->  <!-- CMIREDIR:non-linear_advection_schemes: -->
365  \end{rawhtml}  \end{rawhtml}
# Line 549  $\tau$: {\bf tracer} (argument) Line 550  $\tau$: {\bf tracer} (argument)
550  \subsection{Multi-dimensional advection}  \subsection{Multi-dimensional advection}
551    
552  \begin{figure}  \begin{figure}
553  \resizebox{5.5in}{!}{\includegraphics{part2/advect-2d-lo-diag.eps}}  \resizebox{5.5in}{!}{\includegraphics{s_algorithm/figs/advect-2d-lo-diag.eps}}
554  \caption{  \caption{
555  Comparison of advection schemes in two dimensions; diagonal advection  Comparison of advection schemes in two dimensions; diagonal advection
556  of a resolved Gaussian feature. Courant number is 0.01 with  of a resolved Gaussian feature. Courant number is 0.01 with
# Line 570  lines). Line 571  lines).
571  \end{figure}  \end{figure}
572    
573  \begin{figure}  \begin{figure}
574  \resizebox{5.5in}{!}{\includegraphics{part2/advect-2d-mid-diag.eps}}  \resizebox{5.5in}{!}{\includegraphics{s_algorithm/figs/advect-2d-mid-diag.eps}}
575  \caption{  \caption{
576  Comparison of advection schemes in two dimensions; diagonal advection  Comparison of advection schemes in two dimensions; diagonal advection
577  of a resolved Gaussian feature. Courant number is 0.27 with  of a resolved Gaussian feature. Courant number is 0.27 with
# Line 591  lines). Line 592  lines).
592  \end{figure}  \end{figure}
593    
594  \begin{figure}  \begin{figure}
595  \resizebox{5.5in}{!}{\includegraphics{part2/advect-2d-hi-diag.eps}}  \resizebox{5.5in}{!}{\includegraphics{s_algorithm/figs/advect-2d-hi-diag.eps}}
596  \caption{  \caption{
597  Comparison of advection schemes in two dimensions; diagonal advection  Comparison of advection schemes in two dimensions; diagonal advection
598  of a resolved Gaussian feature. Courant number is 0.47 with  of a resolved Gaussian feature. Courant number is 0.47 with
# Line 665  $W$: {\bf rTrans} (local) Line 666  $W$: {\bf rTrans} (local)
666  \end{minipage} }  \end{minipage} }
667    
668  \begin{figure}  \begin{figure}
669  \resizebox{3.5in}{!}{\includegraphics{part2/multiDim_CS.eps}}  \resizebox{3.5in}{!}{\includegraphics{s_algorithm/figs/multiDim_CS.eps}}
670  \caption{Muti-dimensional advection time-stepping with Cubed-Sphere topology  \caption{Muti-dimensional advection time-stepping with Cubed-Sphere topology
671  \label{fig:advect-multidim_cs}  \label{fig:advect-multidim_cs}
672  }  }
673  \end{figure}  \end{figure}
674    
675  \section{Comparison of advection schemes}  \section{Comparison of advection schemes}
676  \label{sect:tracer_advection_schemes}  \label{sec:tracer_advection_schemes}
677  \begin{rawhtml}  \begin{rawhtml}
678  <!-- CMIREDIR:comparison_of_advection_schemes: -->  <!-- CMIREDIR:comparison_of_advection_schemes: -->
679  \end{rawhtml}  \end{rawhtml}
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