Courant condition implemented for timestep, as described in documentation.

This hasn't been very well tested yet.


git-svn-id: http://svn.cactuscode.org/arrangements/CactusBase/Time/trunk@11 5633253d-7678-4964-a54d-f87795f8ee59

1 files changed, 46 insertions, 8 deletions

diff --git a/doc/documention.tex b/doc/documention.tex
index 4f32b81..316d514 100644
--- a/doc/documention.tex
+++ b/doc/documention.tex
@@ -10,19 +10,57 @@
 
 \section{Purpose}
 
-This, currently very simple, thorn provides a routine for calculating
-the timestep for an evolution based on the spatial Cartesian grid spacing.
-This thorn will be extended in the future to include features like
-a dynamic Courant condition. The thorn works for up to 3 spatial 
-dimensions.
-
+This thorn provides a routines for calculating
+the timestep for an evolution based on the spatial Cartesian grid spacing and
+a wave speed. 
 \section{Comments}
 
-The timestep, which is passed into the Cactus variable {\tt cctk\_delta\_time},
- is calculated by the algorithm
+There are currently two methods for calculating the timestep, either the
+simple courant method, or a dynamic courant method. The method is chosen
+using the keyword parameter {\tt time::method}
+The timestep,  is passed into the Cactus variable {\tt cctk\_delta\_time}.
+Both timesteps are based on the Courant condition, which states that for 
+numerical stability, the chosen timestep should satisfy
+$$
+\Delta t \le \mbox{min}(\Delta x^i)/\mbox{wave speed}/\sqrt(\mbox{dim})
+$$
+
+The two methods currently implemented are:
+\begin{itemize}
+
+\item {\tt time::method = "standard"} (this is the default). The timestep is calculated once
+   at the start of the run in the {\tt BASEGRID} timebin, and is then held static
+   throughout the run. The algorithm, which uses the parameter {\tt time::dtfac} is
 $$
 \Delta t = \mbox{\tt dtfac} * \mbox{min}(\Delta x^i)
 $$
+	Note that the parameter {\tt dtfac} should take into account the dimension
+        of the space being used, and the wave speed.
+
+\item {\tt time::method = "courant"}. The timestep is calculated dynamically at the
+	start of each iteration in the {\tt PRESTEP} timebin. The algorithm is
+$$
+\Delta t = \mbox{\tt courant\_fac} * \mbox{min}(\Delta x^i)/\mbox{maximum wavespeed}/\sqrt(\mbox{dim})
+$$
+
+
+\item {\tt time::method = "courant\_time"}. The timestep is calculated dynamically at the
+    start of each iteration in the {\tt PRESTEP} timebin. The algorithm is
+$$
+\Delta t = \mbox{\tt courant\_fac} * \mbox{minimum time to cross a zone}/\sqrt(\mbox{dim})
+$$
+
+\section{Technical Details}
+
+If a dynamic {\tt courant} condition is selected, a thorn must set the protected variable
+{\tt courant\_wave\_speed} for the maximum wave speed before Time sets the timestep. 
+
+If a dynamic {\tt courant_time} condition is selected, a thorn must set the protected variable
+{\tt courant\_time} for the minimum time for a wave to cross a zone
+ before Time sets the timestep. 
+
+\end{itemize}
+