--- manual/s_algorithm/text/tracer.tex 2001/11/13 18:15:26 1.10 +++ manual/s_algorithm/text/tracer.tex 2002/05/06 19:19:31 1.13 @@ -1,8 +1,8 @@ -% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/tracer.tex,v 1.10 2001/11/13 18:15:26 adcroft Exp $ +% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/tracer.tex,v 1.13 2002/05/06 19:19:31 adcroft Exp $ % $Name: $ \section{Tracer equations} -\label{sec:tracer_equations} +\label{sect:tracer_equations} The basic discretization used for the tracer equations is the second order piece-wise constant finite volume form of the forced @@ -15,7 +15,7 @@ described here. \subsection{Time-stepping of tracers: ABII} -\label{sec:tracer_equations_abII} +\label{sect:tracer_equations_abII} The default advection scheme is the centered second order method which requires a second order or quasi-second order time-stepping scheme to @@ -123,6 +123,7 @@ \section{Linear advection schemes} +\label{sect:tracer-advection} \begin{figure} \resizebox{5.5in}{!}{\includegraphics{part2/advect-1d-lo.eps}} @@ -387,7 +388,7 @@ r = \frac{ \tau_{i+1} - \tau_{i} }{ \tau_{i} - \tau_{i-1} } & \forall & u < 0 \end{eqnarray} as it's argument. There are many choices of limiter function but we -only provide the Superbee limiter \cite{Roe85}: +only provide the Superbee limiter \cite{roe:85}: \begin{equation} \psi(r) = \max[0,\min[1,2r],\min[2,r]] \end{equation} @@ -449,7 +450,7 @@ The DST3 method described above must be used in a forward-in-time manner and is stable for $0 \le |c| \le 1$. Although the scheme -appears to be forward-in-time, it is in fact second order in time and +appears to be forward-in-time, it is in fact third order in time and the accuracy increases with the Courant number! For low Courant number, DST3 produces very similar results (indistinguishable in Fig.~\ref{fig:advect-1d-lo}) to the linear third order method but for