/[MITgcm]/manual/s_algorithm/text/time_stepping.tex
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revision 1.14 by adcroft, Wed Nov 14 21:07:13 2001 UTC revision 1.15 by cnh, Thu Feb 28 19:32:19 2002 UTC
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1  % $Header$  % $Header$
2  % $Name$  % $Name$
3    
4    This chapter lays out the numerical schemes that are
5    employed in the core MITgcm algorithm. Whenever possible
6    links are made to actual program code in the MITgcm implementation.
7    The chapter begins with a discussion of the temporal discretization
8    used in MITgcm. This discussion is followed by sections that
9    describe the spatial discretization. The schemes employed for momentum
10    terms are described first, afterwards the schemes that apply to
11    passive and dynamically active tracers are described.
12    
13    
14    \section{Time-stepping}
15  The equations of motion integrated by the model involve four  The equations of motion integrated by the model involve four
16  prognostic equations for flow, $u$ and $v$, temperature, $\theta$, and  prognostic equations for flow, $u$ and $v$, temperature, $\theta$, and
17  salt/moisture, $S$, and three diagnostic equations for vertical flow,  salt/moisture, $S$, and three diagnostic equations for vertical flow,
# Line 70  temporary.} Line 81  temporary.}
81  \begin{figure}  \begin{figure}
82  \begin{center} \fbox{ \begin{minipage}{4.5in} \begin{tabbing}  \begin{center} \fbox{ \begin{minipage}{4.5in} \begin{tabbing}
83  aaa \= aaa \= aaa \= aaa \= aaa \= aaa \kill  aaa \= aaa \= aaa \= aaa \= aaa \= aaa \kill
84  FORWARD\_STEP \\  \proclink{FORWARD\_STEP}{../code/._model_src_forward_step.F} \\
85  \> DYNAMICS \\  \> DYNAMICS \\
86  \>\> TIMESTEP \` $u^*$,$v^*$ (\ref{eq:ustar-rigid-lid},\ref{eq:vstar-rigid-lid}) \\  \>\> TIMESTEP \` $u^*$,$v^*$ (\ref{eq:ustar-rigid-lid},\ref{eq:vstar-rigid-lid}) \\
87  \> SOLVE\_FOR\_PRESSURE \\  \> SOLVE\_FOR\_PRESSURE \\
# Line 162  The correspondence to the code is as fol Line 173  The correspondence to the code is as fol
173  \item  \item
174  the prognostic phase, equations \ref{eq:ustar-rigid-lid} and \ref{eq:vstar-rigid-lid},  the prognostic phase, equations \ref{eq:ustar-rigid-lid} and \ref{eq:vstar-rigid-lid},
175  stepping forward $u^n$ and $v^n$ to $u^{*}$ and $v^{*}$ is coded in  stepping forward $u^n$ and $v^n$ to $u^{*}$ and $v^{*}$ is coded in
176  {\em TIMESTEP.F}  \proclink{TIMESTEP}{../code/._model_src_timestep.F}
177  \item  \item
178  the vertical integration, $H \widehat{u^*}$ and $H  the vertical integration, $H \widehat{u^*}$ and $H
179  \widehat{v^*}$, divergence and inversion of the elliptic operator in  \widehat{v^*}$, divergence and inversion of the elliptic operator in
180  equation \ref{eq:elliptic} is coded in {\em  equation \ref{eq:elliptic} is coded in
181  SOLVE\_FOR\_PRESSURE.F}  \proclink{SOLVE\_FOR\_PRESSURE}{../code/._model_src_solve_for_pressure.F}
182  \item  \item
183  finally, the new flow field at time level $n+1$ given by equations  finally, the new flow field at time level $n+1$ given by equations
184  \ref{eq:un+1-rigid-lid} and \ref{eq:vn+1-rigid-lid} is calculated in {\em CORRECTION\_STEP.F}.  \ref{eq:un+1-rigid-lid} and \ref{eq:vn+1-rigid-lid} is calculated in
185    \proclink{CORRECTION\_STEP}{../code/._model_src_correction_step.F}.
186  \end{itemize}  \end{itemize}
187  The calling tree for these routines is given in  The calling tree for these routines is given in
188  Fig.~\ref{fig:call-tree-pressure-method}.  Fig.~\ref{fig:call-tree-pressure-method}.
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