/[MITgcm]/manual/s_algorithm/text/tracer.tex
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revision 1.20 by jmc, Thu Jul 7 21:36:34 2005 UTC revision 1.23 by jmc, Tue Jan 15 23:52:12 2008 UTC
# Line 627  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 664  $W$: {\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}  \label{sect:tracer_advection_schemes}
# Line 678  $W$: {\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/$\tau$\\     $3^{rd}$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       \hline
698     $3^{rd}$order DST & 30 &  No & Yes & 5 pts & linear/$\tau$, non-linear/v\\     $3^{rd}$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 \\
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