| 2 |
% $Name$ |
% $Name$ |
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\section{Tracer equations} |
\section{Tracer equations} |
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\label{sec:tracer_equations} |
\label{sect:tracer_equations} |
| 6 |
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| 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 |
| 15 |
described here. |
described here. |
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|
|
| 17 |
\subsection{Time-stepping of tracers: ABII} |
\subsection{Time-stepping of tracers: ABII} |
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\label{sec:tracer_equations_abII} |
\label{sect:tracer_equations_abII} |
| 19 |
|
|
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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 |
| 123 |
|
|
| 124 |
|
|
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\section{Linear advection schemes} |
\section{Linear advection schemes} |
| 126 |
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\label{sect:tracer-advection} |
| 127 |
|
|
| 128 |
\begin{figure} |
\begin{figure} |
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\resizebox{5.5in}{!}{\includegraphics{part2/advect-1d-lo.eps}} |
\resizebox{5.5in}{!}{\includegraphics{part2/advect-1d-lo.eps}} |
| 388 |
r = \frac{ \tau_{i+1} - \tau_{i} }{ \tau_{i} - \tau_{i-1} } & \forall & u < 0 |
r = \frac{ \tau_{i+1} - \tau_{i} }{ \tau_{i} - \tau_{i-1} } & \forall & u < 0 |
| 389 |
\end{eqnarray} |
\end{eqnarray} |
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as it's argument. There are many choices of limiter function but we |
as it's argument. There are many choices of limiter function but we |
| 391 |
only provide the Superbee limiter \cite{Roe85}: |
only provide the Superbee limiter \cite{roe:85}: |
| 392 |
\begin{equation} |
\begin{equation} |
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\psi(r) = \max[0,\min[1,2r],\min[2,r]] |
\psi(r) = \max[0,\min[1,2r],\min[2,r]] |
| 394 |
\end{equation} |
\end{equation} |
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