From 08a501eeaf8c9ba3d8029ac138138a70ece50b44 Mon Sep 17 00:00:00 2001 From: allen Date: Thu, 7 Dec 2000 16:00:45 +0000 Subject: Fixed typo git-svn-id: http://svn.cactuscode.org/arrangements/CactusBase/Time/trunk@29 5633253d-7678-4964-a54d-f87795f8ee59 --- doc/documentation.tex | 84 +++++++++++++++++++++++++++++++++++++++++++++++++++ doc/documention.tex | 84 --------------------------------------------------- 2 files changed, 84 insertions(+), 84 deletions(-) create mode 100644 doc/documentation.tex delete mode 100644 doc/documention.tex diff --git a/doc/documentation.tex b/doc/documentation.tex new file mode 100644 index 0000000..44038b7 --- /dev/null +++ b/doc/documentation.tex @@ -0,0 +1,84 @@ +\documentclass{article} +\begin{document} + +\title{Time} +\author{Gabrielle Allen} +\date{1999} +\maketitle + +\abstract{Calculates the timestep used for an evolution} + +\section{Purpose} + +This thorn provides a routines for calculating +the timestep for an evolution based on the spatial Cartesian grid spacing and +a wave speed. + +\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::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 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 +$$ +\Delta t = \mbox{\tt courant\_fac} * \mbox{min}(\Delta x^i)/\mbox{courant\_wave\_speed}/\sqrt(\mbox{dim}) +$$ + 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::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 +$$ +\Delta t = \mbox{\tt courant\_fac} * \mbox{\tt courant\_min\_time}/\sqrt(\mbox{dim}) +$$ + 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} + +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. + +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 +$$ +\Delta t \le \mbox{min}(\Delta x^i)/\mbox{wave speed}/\sqrt(\mbox{dim}) +$$ + + +\end{itemize} + + + + + + +% Automatically created from the ccl files by using gmake thorndoc +\include{interface} +\include{param} +\include{schedule} + +\end{document} diff --git a/doc/documention.tex b/doc/documention.tex deleted file mode 100644 index 44038b7..0000000 --- a/doc/documention.tex +++ /dev/null @@ -1,84 +0,0 @@ -\documentclass{article} -\begin{document} - -\title{Time} -\author{Gabrielle Allen} -\date{1999} -\maketitle - -\abstract{Calculates the timestep used for an evolution} - -\section{Purpose} - -This thorn provides a routines for calculating -the timestep for an evolution based on the spatial Cartesian grid spacing and -a wave speed. - -\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::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 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 -$$ -\Delta t = \mbox{\tt courant\_fac} * \mbox{min}(\Delta x^i)/\mbox{courant\_wave\_speed}/\sqrt(\mbox{dim}) -$$ - 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::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 -$$ -\Delta t = \mbox{\tt courant\_fac} * \mbox{\tt courant\_min\_time}/\sqrt(\mbox{dim}) -$$ - 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} - -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. - -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 -$$ -\Delta t \le \mbox{min}(\Delta x^i)/\mbox{wave speed}/\sqrt(\mbox{dim}) -$$ - - -\end{itemize} - - - - - - -% Automatically created from the ccl files by using gmake thorndoc -\include{interface} -\include{param} -\include{schedule} - -\end{document} -- cgit v1.2.3