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\section{Linear advection schemes} |
\section{Linear advection schemes} |
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\label{sect:tracer-advection} |
\label{sect:tracer-advection} |
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\begin{rawhtml} |
\begin{rawhtml} |
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<!-- CMIREDIR:linear_advection_schemes: --> |
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\end{rawhtml} |
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\begin{figure} |
\begin{figure} |
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\section{Non-linear advection schemes} |
\section{Non-linear advection schemes} |
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\begin{rawhtml} |
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<!-- CMIREDIR:non-linear_advection_schemes: --> |
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\end{rawhtml} |
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Non-linear advection schemes invoke non-linear interpolation and are |
Non-linear advection schemes invoke non-linear interpolation and are |
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widely used in computational fluid dynamics (non-linear does not refer |
widely used in computational fluid dynamics (non-linear does not refer |
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\section{Comparison of advection schemes} |
\section{Comparison of advection schemes} |
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\begin{table}[htb] |
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\centering |
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\begin{tabular}[htb]{|l|c|c|c|c|l|} |
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\hline |
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Advection Scheme & code & use & use Multi- & Stencil & comments \\ |
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& & A.B. & dimension & (1 dim) & \\ |
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\hline \hline |
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centered $2^{nd}$order & 2 & Yes & No & 3 pts & linear \\ |
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\hline |
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$3^{rd}$order upwind & 3 & Yes & No & 5 pts & linear/tracer\\ |
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\hline |
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centered $4^{th}$order & 4 & Yes & No & 5 pts & linear \\ |
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\hline \hline |
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% Lax-Wendroff & 10 & No & Yes & 3 pts & linear/tracer, non-linear/flow\\ |
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% \hline |
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$3^{rd}$order DST & 30 & No & Yes & 5 pts & linear/tracer, non-linear/flow\\ |
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\hline \hline |
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$2^{nd}$order Flux Limiters & 77 & No & Yes & 5 pts & non-linear \\ |
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\hline |
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$3^{nd}$order DST Flux limiter & 33 & No & Yes & 5 pts & non-linear \\ |
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\hline |
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\end{tabular} |
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\caption{Summary of the different advection schemes available in MITgcm. |
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``A.B.'' stands for Adams-Bashforth and ``DST'' for direct space time. |
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The code corresponds to the number used to select the corresponding |
| 689 |
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advection scheme in the parameter file (e.g., {\em tempAdvScheme=3} in |
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file {\em data} selects the $3^{rd}$ order upwind advection scheme |
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for temperature). |
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} |
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\label{tab:advectionShemes_summary} |
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\end{table} |
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Figs.~\ref{fig:advect-2d-lo-diag}, \ref{fig:advect-2d-mid-diag} and |
Figs.~\ref{fig:advect-2d-lo-diag}, \ref{fig:advect-2d-mid-diag} and |
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\ref{fig:advect-2d-hi-diag} show solutions to a simple diagonal |
\ref{fig:advect-2d-hi-diag} show solutions to a simple diagonal |
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advection problem using a selection of schemes for low, moderate and |
advection problem using a selection of schemes for low, moderate and |
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