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diff --git a/doc/documention.tex b/doc/documention.tex index 5629beb..44038b7 100644 --- a/doc/documention.tex +++ b/doc/documention.tex @@ -13,51 +13,61 @@ 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} - -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: +\section{Description} + +Thorn {\tt Time} uses one of four methods to decide on the timestep +to be used for the simulation. The method is chosen using the +keyword parameter {\tt time::timestep\_method}. (Note: In releases Beta 8 and +earlier the parameter used was {\tt time::courant\_method} \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 +\item{} {\tt time::timestep\_method = ``given''} The timestep is fixed to the + value of the parameter {\tt time::timestep}. + +\item{} {\tt time::timestep\_method = ``courant\_static''} This is the default + method, which calculates the timestep once at the start of the + simulation, based on a simple courant type condition using + the spatial gridsizes and the parameter {\tt time::dtfac}. $$ \Delta t = \mbox{\tt dtfac} * \mbox{min}(\Delta x^i) $$ - 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 + Note that it is up to the user to custom {\tt dtfac} to take + into account the dimension of the space being used, and the wave speed. + +\item{} {\tt time::timestep\_method = ``courant\_speed''} This choice implements a + dynamic courant type condition, the timestep being set before each + timestep using the spatial dimension of the grid, the spatial grid sizes, the + parameter {\tt courant\_fac} and the grid variable {\tt courant\_wave\_speed}. + The algorithm used is $$ -\Delta t = \mbox{\tt courant\_fac} * \mbox{min}(\Delta x^i)/\mbox{maximum wavespeed}/\sqrt(\mbox{dim}) +\Delta t = \mbox{\tt courant\_fac} * \mbox{min}(\Delta x^i)/\mbox{courant\_wave\_speed}/\sqrt(\mbox{dim}) $$ + For this algorithm to be successful, the variable {\tt courant\_wave\_speed} + must have been set by a thorn to the maximum wave speed on the grid. - -\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 +\item{} {\tt time::timestep\_method = ``courant\_time''} This choice is similar to the + method {\tt courant\_speed} above, in implementing a dynamic timestep. + However the timestep is chosen using $$ -\Delta t = \mbox{\tt courant\_fac} * \mbox{minimum time to cross a zone}/\sqrt(\mbox{dim}) +\Delta t = \mbox{\tt courant\_fac} * \mbox{\tt courant\_min\_time}/\sqrt(\mbox{dim}) $$ + where the grid variable {\tt courant\_min\_time} must be set by a thorn to + the minimum time for a wave to cross a gridzone. + +\end{itemize} -\section{Technical Details} +In all cases, Thorn {\tt Time} sets the Cactus variable {\tt cctk\_delta\_time} +which is passed as part of the macro {\tt CCTK\_ARGUMENTS} to thorns called +by the scheduler. -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. +Note that for hyperbolic problems, the Courant condition gives a minimum +requirement for stability, namely that the numerical domain of dependency +must encompass the physical domain of dependency, or +$$ +\Delta t \le \mbox{min}(\Delta x^i)/\mbox{wave speed}/\sqrt(\mbox{dim}) +$$ -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} |