From c26c84861a4cb282162aca3b2b1678f87622dc35 Mon Sep 17 00:00:00 2001 From: allen Date: Thu, 9 May 2002 11:50:57 +0000 Subject: changed to Einstein2 git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinInitialData/IDAnalyticBH/trunk@115 6a3ddf76-46e1-4315-99d9-bc56cac1ef84 --- doc/documentation.tex | 70 +++++++++++++++++++++++++-------------------------- 1 file changed, 35 insertions(+), 35 deletions(-) diff --git a/doc/documentation.tex b/doc/documentation.tex index deafab2..5493b0b 100644 --- a/doc/documentation.tex +++ b/doc/documentation.tex @@ -62,7 +62,7 @@ initial dataset for black hole evolution that can be specified analytically in terms of the metric, $g_{ab}$, and extrinsic curvature, $K_{ab}$. -The thorn extends the \texttt{einstein::initial\_data} parameter by +The thorn extends the \texttt{admbase::initial\_data} parameter by adding the following datasets: \begin{description} \item[\texttt{schwarzschild}] Schwarzschild, in isotropic @@ -75,10 +75,10 @@ Initial data for lapse and shift can also be specified in this thorn.\\ The Cactus grid-functions corresponding to the initial data are -inherited from the thorn \texttt{CactusEinstein/Einstein}, along with -the conformal factor grid-function, \texttt{psi}, and its derivatives -which are optionally set based on the value of the parameter -\texttt{einstein::use\_conformal}.\\ +inherited from the thorn \texttt{CactusEinstein/ADMBase}, along with +the conformal factor grid-function, \texttt{psi} from \texttt{CactusEinstein/StaticConformal}, and its derivatives +which are optionally set based on the value of the parameters +\texttt{admbase::metric\_type} and \texttt{staticconformal::conformal\_storage}.\\ The \texttt{IDAnalyticBH} has been written and augmented over an number of years by many Cactus authors. These include John Baker, Steve Brandt, @@ -90,7 +90,7 @@ associated parameters in turn. The Schwarzschild metric corresponds to a single, static, black hole. If the Cactus metric is specified as a conformal metric (by setting -\texttt{einstein::use\_conformal="yes"}), then the metric is +\texttt{admbase::metric\_type="yes"}), then the metric is set using isotropic coordinates \cite{mtw-isotropic}: \begin{equation} ds^2 = -\left(\frac{2r - M}{2r + M}\right)^2 @@ -109,19 +109,19 @@ The mass is specified using the parameter \texttt{idanalyticbh::mass}. The black hole is assumed to reside at the origin of the grid, corresponding to the location $x=y=z=0$.\\ -If the \texttt{einstein::use\_conformal} parameter has been set, then -the metric grid-functions (\texttt{einstein::gxx}, $\ldots$, -\texttt{einstein::gzz}) are given as $\delta_{ab}$, and the conformal -factor \texttt{einstein::psi} is set to the value specified +If the \texttt{admbase::metric\_type} parameter has been set to {\tt static conformal}, then +the metric grid-functions (\texttt{admbase::gxx}, $\ldots$, +\texttt{admbase::gzz}) are given as $\delta_{ab}$, and the conformal +factor \texttt{staticconformal::psi} is set to the value specified above. The derivatives of the conformal factor -(\texttt{einstein::psix}, etc.) are determined analytically. +(\texttt{staticconformal::psix}, etc.) are determined analytically. In order to give the lapse an initial profile which corresponds to isotropic lapse of the $4$-metric specified above, use the parameter \begin{verbatim} idanalyticbh::initial_lapse = "schwarz" \end{verbatim} -This will cause the \texttt{einstein::alp} grid-function to be +This will cause the \texttt{admbase::alp} grid-function to be initialised to the value: \begin{equation} \alpha = \frac{2r - M}{2r + M}. @@ -129,9 +129,9 @@ initialised to the value: Note that the Schwarzschild data has the following non-standard -behaviour in response to the \texttt{einstein::use\_conformal} +behaviour in response to the \texttt{admbase::metric\_type} parameter. If the \emph{physical} metric is requested -(ie. \texttt{use\_conformal} is set to \texttt{"no"}) then a +(ie. \texttt{metric\_type} is set to \texttt{"physical"}) then a \emph{different} form of the Schwarzschild metric is set: Schwarzschild coordinates are set instead of the isotropic coordinates: @@ -145,12 +145,12 @@ black hole of mass $m=1$, using an initial lapse of $\alpha=1$, you could modify your parameter file as follows: \begin{verbatim} - ActiveThorns = "... Einstein IDAnalyticBH ..." + ActiveThorns = "... ADMBase StaticConformal IDAnalyticBH ..." - einstein::use_conformal = "yes" + admbase::metric_type = "static conformal" - einstein::initial_data = "schwarzschild" - einstein::initial_lapse = "one" # or "schwarz" for isotropic lapse + admbase::initial_data = "schwarzschild" + admbase::initial_lapse = "one" # or "schwarz" for isotropic lapse idanalyticbh::mass = 1.0 \end{verbatim} @@ -179,13 +179,13 @@ respectively. \emph{(Note that the default values for these parameters are $M=2$ and $a=0.1$.)} The black hole is assumed to reside at the centre of the coordinate system, at $x=y=z=0$. -The \texttt{einstein::use\_conformal} parameter can be used to specify +The \texttt{admbase::metric\_type} parameter can be used to specify whether the metric should be conformal or not. If the metric is conformal, then $\psi$ is initialised as a separate grid function, and it's first and second derivatives are calculated analytically and also stored as grid functions. Otherwise, the conformal factor is multiplied through in the expression for the 3-metric before the -values of the \texttt{einstein::metric} variables are set. The +values of the \texttt{admbase::metric} variables are set. The extrinsic curvature is also determined analytically. The gauge can be set to the Kerr lapse and shift with the parameters @@ -206,13 +206,13 @@ where A set of parameters which initialise an evolution to use the Kerr intial data with mass $M=1$ and angular momentum $a=0.3$ are: \begin{verbatim} - ActiveThorns = "... Einstein IDAnalyticBH ..." + ActiveThorns = "... ADMBase StaticConformal IDAnalyticBH ..." - einstein::use_conformal = "yes" + admbase::metric_type = "static conformal" - einstein::initial_data = "kerr" - einstein::initial_lapse = "kerr" - einstein::initial_shift = "kerr" + admbase::initial_data = "kerr" + admbase::initial_lapse = "kerr" + admbase::initial_shift = "kerr" idanalyticbh::mass = 1.0 idanalyticbh::a_kerr = 0.3 @@ -283,18 +283,18 @@ This quantity is determined automatically and written to standard output. If the conformal form of the metric is used (via the -\texttt{einstein::use\_conformal} parameter), then derivatives of the +\texttt{admbase::metric\_type} parameter), then derivatives of the conformal factor are computed analytically from the derivatives of the above expression for $\psi$. To make use of the two black hole initial data, a variation of the following set of parameters can be used: \begin{verbatim} - ActiveThorns = "... Einstein IDAnalyticBH ..." + ActiveThorns = "... ADMBase StaticConformal IDAnalyticBH ..." - einstein::use_conformal = "yes" + admbase::metric_type = "static conformal" - einstein::initial_data = "misner_bh" + admbase::initial_data = "misner_bh" idanalyticbh::mu = 2.2 \end{verbatim} @@ -337,11 +337,11 @@ stencil is hardcoded at $dx=10^-6$. As an example, a parameter file implementing 3 Misner black holes on a circle of radius $\cosh 4$ would use the following parameters: \begin{verbatim} - ActiveThorns = "... Einstein IDAnalyticBH ..." + ActiveThorns = "... ADMBase StaticConformal IDAnalyticBH ..." - einstein::use_conformal = "yes" + admbase::metric_type = "static conformal" - einstein::initial_data = "multiple_misner_bh" + admbase::initial_data = "multiple_misner_bh" idanalyticbh::misner_nbh = 3 idanalyticbh::mu = 4 @@ -389,11 +389,11 @@ To initialise a run with a pair of Brill-Lindquist black holes with masses $1$ and $2$ and located at $\pm 1$ on the $y$-axis, a set of parameters such as the following could be used: \begin{verbatim} - ActiveThorns = "... Einstein IDAnalyticBH ..." + ActiveThorns = "... ADMBase StaticConformal IDAnalyticBH ..." - einstein::use_conformal = "yes" + admbase::metric_type = "static conformal" - einstein::initial_data = "bl_bh" + admbase::initial_data = "bl_bh" idanalyticbh::bl_nbh = 2 -- cgit v1.2.3