[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 67)

[cott at tapir.caltech.edu]

User: cott
Date: 2011/04/27 01:24 PM

Modified:
 /
  ET.tex
 /local_bibtex/
  ott_references.bib

Log:
 * clean up BSSN section a bit

File Changes:

Directory: /
============

File [modified]: ET.tex
Delta lines: +12 -23
===================================================================
--- ET.tex	2011-04-27 17:58:18 UTC (rev 66)
+++ ET.tex	2011-04-27 18:24:03 UTC (rev 67)
@@ -931,11 +931,12 @@
 In the following, we assume that the reader is familiar with the
 basics of numerical relativity and GR hydrodynamics. Detailed
 introductions to numerical relativity have recently been given by
-Alcubierre~\cite{alcubierre:08}, Baumgarte \& Shapiro~\cite{baumgarte:10},
-and Centrella et al.~\cite{centrella:10}.
+Alcubierre~\cite{alcubierre:08}, Baumgarte \&
+Shapiro~\cite{baumgarte:10}, and Centrella et al.~\cite{centrella:10}.
 GR hydrodynamics has been reviewed by Font~\cite{font:08}. In the
-following, we assume the reader to be familiar with general relativity.
-We assume $G = c = M_\odot = 1$ throughout.
+following, we assume the reader to be familiar with general
+relativity, differential geometry and tensor analysis.  We set $G = c
+= M_\odot = 1$ throughout.
 
 The Einstein Toolkit provides code to evolve the Einstein equations
 \begin{equation}
@@ -957,8 +958,8 @@
 T^{\mu\nu} = \rho h u^\mu u^\nu - g^{\mu\nu} P\,\,,
 \end{equation}
 where $\rho$ is the rest-mass density, $u^\mu$ is the 4-velocity,
-$g^{\mu\nu}$ is the 4-metric, and $h = 1 + \epsilon + P/\rho$ is the
-relativistic specific enthalpy with $\epsilon$ and $P$ being the
+$g^{\mu\nu}$ is the upper 4-metric, and $h = 1 + \epsilon + P/\rho$ is
+the relativistic specific enthalpy with $\epsilon$ and $P$ being the
 specific internal energy and the pressure, respectively.
 
 \subsubsection{Spacetime Curvature Evolution} The Einstein Toolkit
@@ -971,7 +972,11 @@
 \cite{shibata:95,baumgarte:95,alcubierre:00} of the original
 Arnowitt-Deser-Misner (ADM) formalism~\cite{adm:62} is employed.
 
+\codename{McLachlan} uses fourth-order accurate finite differencing
+for the spacetime variables and add a fifth-order Kreiss-Oliger
+dissipation term to remove high frequency noise.
 
+
 The evolved variables are the conformal factor $\Phi$, the conformal
 3-metric $\tilde{\gamma}_{ij}$, the trace $K$ of the extrinsic curvature,
 the trace free extrinsic curvature $A_{ij}$ and the conformal connection
@@ -1120,25 +1125,9 @@
 with a constant $R$ defining the transition radius between the
 interior, where $q\approx1$, and the exterior, where $q$ falls off as
 $1/r$. Eq.~\ref{eq:eta} describes how $q$ appears in the gauge
-parameters. In this paper we use $R=250\,M_\odot$ ($R =
-369.2\,\mathrm{km}$).
+parameters. 
 
-We implement the above BSSN equations and gauge conditions in the
-{\tt McLachlan} code \cite{ES-Brown2007b, ES-mclachlanweb} which is
-freely available as part of the {\tt EinsteinToolkit}. {\tt McLachlan} is
-auto-generated from the definition of the variables and equations in the
-{\tt Mathematica} format by the {\tt Kranc} code generator \cite{kranc04,
-  Husa:2004ip, krancweb}. {\tt Kranc} is a suite of {\tt Mathematica} packages
-comprising a computer algebra toolbox for numerical relativists. {\tt Kranc}
-can be used as a ``rapid prototyping'' system for physicists or
-mathematicians handling complex systems of partial differential
-equations, and through integration into the {\tt Cactus} framework one can
-also produce efficient production codes.
 
-We use fourth-order accurate finite differencing for the spacetime
-variables and add a fifth-order Kreiss-Oliger dissipation term to
-remove high frequency noise. We use a fourth-order Runge-Kutta time
-integrator for all evolved variables.
 
 \subsubsection{Initial Conditions}
 

Directory: /local_bibtex/
=========================

File [modified]: ott_references.bib
Delta lines: +25 -0
===================================================================
--- local_bibtex/ott_references.bib	2011-04-27 17:58:18 UTC (rev 66)
+++ local_bibtex/ott_references.bib	2011-04-27 18:24:03 UTC (rev 67)
@@ -115,3 +115,28 @@
    adsurl = {http://adsabs.harvard.edu/abs/2010RvMP...82.3069C},
 }
 
+ at Article{Muller:2009jx,
+  author =       {M{\"u}ller, Doreen and Br{\"u}gmann, Bernd},
+  title =        {Toward a dynamical shift condition for unequal mass
+                  black hole binary simulations},
+  journal =      {Class. Quantum Grav.},
+  volume =       27,
+  year =         2010,
+  pages =        114008,
+  doi =          {10.1088/0264-9381/27/11/114008},
+  SLACcitation = "%%CITATION = 0912.3125;%%"
+}
+
+ at Article{ES-Schnetter2010a,
+  status =       {refereed},
+  author =       {Erik Schnetter},
+  title =        {Time Step Size Limitation Introduced by the {BSSN}
+                  {Gamma} Driver},
+  journal =      {Class. Quantum Grav.},
+  volume =       27,
+  pages =        167001,
+  year =         2010,
+  receiveddate = {2010-03-04},
+  doi =          {10.1088/0264-9381/27/16/167001},
+}
+