/[MITgcm]/manual/s_algorithm/text/tracer.tex
ViewVC logotype

Diff of /manual/s_algorithm/text/tracer.tex

Parent Directory Parent Directory | Revision Log Revision Log | View Revision Graph Revision Graph | View Patch Patch

revision 1.17 by jmc, Thu Oct 14 19:53:04 2004 UTC revision 1.23 by jmc, Tue Jan 15 23:52:12 2008 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 621  as if in one dimension: Line 627  as if in one dimension:
627  \tau^{n+1/3} & = & \tau^{n}  \tau^{n+1/3} & = & \tau^{n}
628  - \Delta t \left( \frac{1}{\Delta x} \delta_i F^x(\tau^{n})  - \Delta t \left( \frac{1}{\Delta x} \delta_i F^x(\tau^{n})
629             + \tau^{n} \frac{1}{\Delta x} \delta_i u \right) \\             + \tau^{n} \frac{1}{\Delta x} \delta_i u \right) \\
630  \tau^{n+2/3} & = & \tau^{n}  \tau^{n+2/3} & = & \tau^{n+1/3}
631  - \Delta t \left( \frac{1}{\Delta y} \delta_j F^y(\tau^{n+1/3})  - \Delta t \left( \frac{1}{\Delta y} \delta_j F^y(\tau^{n+1/3})
632             + \tau^{n} \frac{1}{\Delta y} \delta_i v \right) \\             + \tau^{n} \frac{1}{\Delta y} \delta_i v \right) \\
633  \tau^{n+3/3} & = & \tau^{n}  \tau^{n+3/3} & = & \tau^{n+2/3}
634  - \Delta t \left( \frac{1}{\Delta r} \delta_k F^x(\tau^{n+2/3})  - \Delta t \left( \frac{1}{\Delta r} \delta_k F^x(\tau^{n+2/3})
635             + \tau^{n} \frac{1}{\Delta r} \delta_i w \right)             + \tau^{n} \frac{1}{\Delta r} \delta_i w \right)
636  \end{eqnarray}  \end{eqnarray}
# Line 658  $W$: {\bf rTrans} (local) Line 664  $W$: {\bf rTrans} (local)
664    
665  \end{minipage} }  \end{minipage} }
666    
667    \begin{figure}
668    \resizebox{3.5in}{!}{\includegraphics{part2/multiDim_CS.eps}}
669    \caption{Muti-dimensional advection time-stepping with Cubed-Sphere topology
670    \label{fig:advect-multidim_cs}
671    }
672    \end{figure}
673    
674  \section{Comparison of advection schemes}  \section{Comparison of advection schemes}
675    \label{sect:tracer_advection_schemes}
676    \begin{rawhtml}
677    <!-- CMIREDIR:comparison_of_advection_schemes: -->
678    \end{rawhtml}
679    
680  \begin{table}[htb]  \begin{table}[htb]
681  \centering  \centering
# Line 668  $W$: {\bf rTrans} (local) Line 684  $W$: {\bf rTrans} (local)
684     Advection Scheme & code & use  & use Multi- & Stencil & comments \\     Advection Scheme & code & use  & use Multi- & Stencil & comments \\
685                      &      & A.B. & dimension & (1 dim) & \\                      &      & A.B. & dimension & (1 dim) & \\
686     \hline \hline     \hline \hline
687       $1^{rst}$order upwind  & 1 &  No & Yes & 3 pts & linear/$\tau$, non-linear/v\\
688       \hline
689     centered $2^{nd}$order & 2 &  Yes & No & 3 pts & linear \\     centered $2^{nd}$order & 2 &  Yes & No & 3 pts & linear \\
690     \hline     \hline
691     $3^{rd}$order upwind   & 3 &  Yes & No & 5 pts & linear/tracer\\     $3^{rd}$order upwind   & 3 &  Yes & No & 5 pts & linear/$\tau$\\
692     \hline     \hline
693     centered $4^{th}$order & 4 &  Yes & No & 5 pts & linear \\     centered $4^{th}$order & 4 &  Yes & No & 5 pts & linear \\
694     \hline \hline     \hline \hline
695  %  Lax-Wendroff       & 10 &  No & Yes & 3 pts & linear/tracer, non-linear/flow\\     $2^{nd}$order DST (Lax-Wendroff)  & 20 &
696  %  \hline                           No & Yes & 3 pts & linear/$\tau$, non-linear/v\\
697     $3^{rd}$order DST & 30 &  No & Yes & 5 pts & linear/tracer, non-linear/flow\\     \hline
698       $3^{rd}$order DST & 30 &  No & Yes & 5 pts & linear/$\tau$, non-linear/v\\
699     \hline \hline     \hline \hline
700     $2^{nd}$order Flux Limiters & 77 &  No & Yes & 5 pts & non-linear \\     $2^{nd}$order Flux Limiters & 77 &  No & Yes & 5 pts & non-linear \\
701     \hline     \hline
# Line 686  $W$: {\bf rTrans} (local) Line 705  $W$: {\bf rTrans} (local)
705   \caption{Summary of the different advection schemes available in MITgcm.   \caption{Summary of the different advection schemes available in MITgcm.
706            ``A.B.'' stands for Adams-Bashforth and ``DST'' for direct space time.            ``A.B.'' stands for Adams-Bashforth and ``DST'' for direct space time.
707            The code corresponds to the number used to select the corresponding            The code corresponds to the number used to select the corresponding
708            advection scheme in the parameter file (e.g., {\em tempAdvScheme=3} in            advection scheme in the parameter file (e.g., {\bf tempAdvScheme}=3 in
709            file {\em data} selects the $3^{rd}$ order upwind advection scheme            file {\em data} selects the $3^{rd}$ order upwind advection scheme
710            for temperature).            for temperature).
711     }     }
Legend:
Removed from v.1.17  
changed lines
  Added in v.1.23
  ViewVC Help
Powered by ViewVC 1.1.22