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

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

Log: * clean up BSSN section a bit

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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%7D, }

+@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;%%" +} + +@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}, +} +