Commits

commits@lists.einsteintoolkit.org

2 participants
6997 discussions

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 164)
by knarf＠cct.lsu.edu 06 Nov '11

06 Nov '11

User: knarf Date: 2011/11/06 12:34 AM Modified: / ET.tex Log: remove page markers File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +4 -2 =================================================================== --- ET.tex 2011-11-06 05:33:06 UTC (rev 163) +++ ET.tex 2011-11-06 05:34:42 UTC (rev 164) @@ -36,11 +36,13 @@ \newcommand{\codename}[1]{\texttt{#1}} \newcommand{\todo}[1]{{\color{red}$\blacksquare$~\textsf{[TODO: #1]}}} \newcommand{\comment}[1]{{\color{blue}$\blacksquare$~\textsf{[Comment: #1]}}} -\newcommand{\pages}[1]{{\color{blue}$\blacksquare$~\textsf{[#1]}}} +%\newcommand{\pages}[1]{{\color{blue}$\blacksquare$~\textsf{[#1]}}} +\newcommand{\pages}[1]{} % Use this macro for sections which are done, so that those comments % can easily be disabled. -\newcommand{\pagesdone}[1]{{\color{green}$\blacksquare$~\textsf{[#1]}}} +%\newcommand{\pagesdone}[1]{{\color{green}$\blacksquare$~\textsf{[#1]}}} +\newcommand{\pagesdone}[1]{} %\newcommand{\pagesdone}[1]{} \newcommand{\BCM}[1]{{\bf \color{blue} [BCM: #1] }} %BCM comments

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 163)
by knarf＠cct.lsu.edu 06 Nov '11

06 Nov '11

User: knarf Date: 2011/11/06 12:33 AM Modified: / ET.tex Log: make sure lines are not broken before citations File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +57 -58 =================================================================== --- ET.tex 2011-11-06 05:30:41 UTC (rev 162) +++ ET.tex 2011-11-06 05:33:06 UTC (rev 163) @@ -122,13 +122,13 @@ in the study of astrophysical systems containing black holes (BHs) and neutron stars (NSs). While the first fully general relativistic (GR) simulations of merging NS-NS binaries were reported in 1999, with further -advances for the next few years \cite{Shibata:1999wm,Shibata:2002jb, +advances for the next few years~\cite{Shibata:1999wm,Shibata:2002jb, Shibata:2003ga,Shibata:2005ss,Shibata:2006nm}, systems containing BHs proved much more numerically intractable until 2005. That year, computational breakthroughs were made in using a generalized harmonic gauge (GHG) \cite{Pretorius:2005gq} and then a ``moving puncture'' approach \cite{Campanelli:2005dd, Baker:2005vv} in the BSSN -(Baumgarte-Shapiro-Shibata-Nakamura) formalism \cite{Shibata:1995we,Baumgarte:1998te} +(Baumgarte-Shapiro-Shibata-Nakamura) formalism~\cite{Shibata:1995we,Baumgarte:1998te} that allowed for the first stable long-term evolutions of moving single and multiple BH systems. These results quickly transformed the field with the ability to effectively evolve the Einstein field equations @@ -147,7 +147,7 @@ Ajith:2007kx} and references therein), comparisons between numerical waveforms~\cite{Baker:2006yw,Baker:2007fb}, determination of the spin of -the remnant BH formed in BH-BH mergers~(e.g, \cite{Campanelli:2006uy, +the remnant BH formed in BH-BH mergers~(e.g,~\cite{Campanelli:2006uy, Campanelli:2006fg,Campanelli:2006fy, Herrmann:2007ex,Rezzolla:2007rz,Berti:2007nw} and references therein), and studies of eccentric BH-BH binaries @@ -159,25 +159,25 @@ settings since the mid-1990s, focusing on BH accretion processes and relativistic jet production and evolution (see, e.g.,~\cite{Font:2008aa} for a review of the numerical formalism, -and \cite{Hawley2009apss} for a review of work on disk and jet models). +and~\cite{Hawley2009apss} for a review of work on disk and jet models). GRMHD coupled with curvature evolution, on the other hand, which is crucial for modeling large-scale bulk dynamics in compact binary or single-star collapse scenarios, has started to produce astrophysically interesting results only in the past $\sim 3-5$ years, enabled primarily by the availability of the long-term stable curvature evolution systems discussed above as well as improved GRMHD -algorithms~(see \cite{Font:2008aa} for a review). +algorithms~(see~\cite{Font:2008aa} for a review). In addition to these developments, substantial progress has been made in using physically motivated equations of state (EOS), -including tabulated versions (e.g., \cite{Pandharipande:1989hn, +including tabulated versions (e.g.,~\cite{Pandharipande:1989hn, Douchin:2001sv,Akmal:1998cf}) and temperature-dependent models -(e.g., \cite{Shen:1998by,Shen:1998gq,Lattimer:1991nc}). Some codes also +(e.g.,~\cite{Shen:1998by,Shen:1998gq,Lattimer:1991nc}). Some codes also incorporate microphysical effects, such as neutrino cooling \cite{Sekiguchi:2011zd}. Many of the successful techniques used to evolve BH-BH binaries have proven to be equally applicable to merging -NS-NS and BH-NS binaries (see, e.g., \cite{Faber:2009zz,Duez:2009yz} for reviews), allowing for further investigations into the former +NS-NS and BH-NS binaries (see, e.g.,~\cite{Faber:2009zz,Duez:2009yz} for reviews), allowing for further investigations into the former and the first full GR simulations of the latter. All recent results use either the GHG formalism (Caltech/Cornell, LSU/BYU/LIU, and Princeton) or BSSN ``moving puncture'' gauge (or variants thereof; AEI/Sissa, Illinois, @@ -185,27 +185,27 @@ refinement, since unigrid models cannot produce accurate long-term evolutions without requiring exorbitant computational resources. Many groups' codes now include GRMHD (used widely for NS-NS mergers, and for BH-NS mergers -in \cite{Chawla:2010sw}, and some include microphysical effects as well. +in~\cite{Chawla:2010sw}, and some include microphysical effects as well. The groups that have reported simulations of NS-NS or BH-NS mergers include: \begin{description} -\item[AEI/Sissa]: BH-NS mergers using GRHD \cite{Loffler:2006nu} and NS-NS -mergers using GRHD \cite{Baiotti:2008ra,Baiotti:2009gk,Baiotti:2010xh, -Baiotti:2011am,Rezzolla:2010fd} and GRMHD \cite{Giacomazzo:2009mp, +\item[AEI/Sissa]: BH-NS mergers using GRHD~\cite{Loffler:2006nu} and NS-NS +mergers using GRHD~\cite{Baiotti:2008ra,Baiotti:2009gk,Baiotti:2010xh, +Baiotti:2011am,Rezzolla:2010fd} and GRMHD~\cite{Giacomazzo:2009mp, Giacomazzo:2010bx,Rezzolla:2011da}. \item[Caltech/Cornell]: A {\em pseudospectral}, GRHD code has been used -to simulate BH-NS mergers \cite{Duez:2008rb,Duez:2009yy,Foucart:2010eq}. -\item[Illinois]: BH-NS mergers using GRHD \cite{Etienne:2007jg,Etienne:2008re} -and NS-NS mergers using GRMHD \cite{Liu:2008xy}. -\item[Jena]: NS-NS mergers using GRHD \cite{Thierfelder:2011yi}. -\item[LSU/BYU/LIU]: BH-NS mergers using GRMHD \cite{Chawla:2010sw} and -NS-NS mergers using GRHD \cite{Anderson:2007kz} -and GRMHD \cite{Anderson:2008zp}. -\item[Princeton]: BH-NS mergers using GRHD \cite{Stephens:2011as}. -\item[Tokyo/Kyoto]: BH-NS mergers using GRHD \cite{Shibata:2006bs, +to simulate BH-NS mergers~\cite{Duez:2008rb,Duez:2009yy,Foucart:2010eq}. +\item[Illinois]: BH-NS mergers using GRHD~\cite{Etienne:2007jg,Etienne:2008re} +and NS-NS mergers using GRMHD~\cite{Liu:2008xy}. +\item[Jena]: NS-NS mergers using GRHD~\cite{Thierfelder:2011yi}. +\item[LSU/BYU/LIU]: BH-NS mergers using GRMHD~\cite{Chawla:2010sw} and +NS-NS mergers using GRHD~\cite{Anderson:2007kz} +and GRMHD~\cite{Anderson:2008zp}. +\item[Princeton]: BH-NS mergers using GRHD~\cite{Stephens:2011as}. +\item[Tokyo/Kyoto]: BH-NS mergers using GRHD~\cite{Shibata:2006bs, Shibata:2006ks,Shibata:2007zm,Yamamoto:2008js,Shibata:2009cn, Kyutoku:2010zd,Shibata:2010zz} and NS-NS mergers using GRHD \cite{Yamamoto:2008js,Kiuchi:2009jt, Kiuchi:2010ze,Hotokezaka:2011dh}, -most recently with the inclusion of neutrino cooling \cite{Sekiguchi:2011zd}. +most recently with the inclusion of neutrino cooling~\cite{Sekiguchi:2011zd}. \todo{Check for updates to list before submission!} \end{description} @@ -214,10 +214,10 @@ in NSs. GRHD has been used to study, among many other applications, massive stars collapsing to protoneutron stars \cite{Ott:2006eu,Ott:2006eh,Shibata:2004kb}, the collapse of rotating, -hypermassive NSs to BHs in 2D and 3D (see, e.g., \cite{Shibata:2006hr, +hypermassive NSs to BHs in 2D and 3D (see, e.g.,~\cite{Shibata:2006hr, Shibata:1999yx,Duez:2005sf,Duez:2005cj,Baiotti:2004wn,Baiotti:2005vi, Baiotti:2006wn}), and non-axisymmetric instabilities in -rapidly rotating polytropic NS models \cite{Shibata:1999yx,Baiotti:2006wn, +rapidly rotating polytropic NS models~\cite{Shibata:1999yx,Baiotti:2006wn, Manca:2007ca}. In parallel to the advances in both our physical understanding of @@ -226,22 +226,22 @@ aim of providing a computational core that can enable the new science, broaden the community, facilitate interdisciplinary research and take advantage of emerging petascale computers and advanced cyberinfrastructure: -the {\tt Cactus} computational toolkit \cite{Cactuscode:web}. While it was +the {\tt Cactus} computational toolkit~\cite{Cactuscode:web}. While it was developed in large part by computer scientists, its development was driven by the direct input from other fields, especially numerical relativity, succeeding in applying expertise in computer science directly to problems in numerical relativity. This success prompted usage of the {\tt Cactus} computational toolkit in other -areas, such as ocean forecast models \cite{Djikstra2005} and chemical reaction -simulations \cite{Camarda2001}. At the same time, the growing +areas, such as ocean forecast models~\cite{Djikstra2005} and chemical reaction +simulations~\cite{Camarda2001}. At the same time, the growing number of results in numerical relativity increased the need for commonly available utilities such as comparison and analysis tools, typically those specifically designed for astrophysical problems. Including them within the {\tt Cactus} computational toolkit was not felt to fit within its rapidly expanding scope. This triggered -the creation of the Einstein Toolkit \cite{EinsteinToolkit:web}. While large +the creation of the Einstein Toolkit~\cite{EinsteinToolkit:web}. While large parts of the Einstein toolkit presently do make use of the {\tt Cactus} toolkit, this is not an requirement at all, and other contributions are welcome and have been accepted. @@ -281,9 +281,8 @@ \item {\bf Equation of state (EOS), microphysics, and radiation transport}. Most presently published 3D GR(M)HD simulations, with the - exceptions of recent work on massive star collapse - \cite{???}\todo{Citation?} and binary mergers - (see, e.g., \cite{Sekiguchi:2011zd}), + exceptions of recent work on massive star collapse~\cite{???}\todo{Citation?} and binary mergers + (see, e.g.,~\cite{Sekiguchi:2011zd}), relied on a simple zero-temperature descriptions of NS stellar structure, with many assuming simple polytropic forms. Such EOSs are computationally @@ -299,7 +298,7 @@ the cooling of NS-NS merger remnants and must not be left out when attempting to accurately model such events. Only few studies have incorporated neutrino and/or photon transport and interactions in - approximate ways (see, e.g., \cite{Ott:2006eu,Farris:2008fe,Sekiguchi:2011zd}) \todo{Cite more}. + approximate ways (see, e.g.,~\cite{Ott:2006eu,Farris:2008fe,Sekiguchi:2011zd}) \todo{Cite more}. \item {\bf High-order schemes and AMR\@}. Numerical accuracy is a central issue in long-term GR(M)HD simulations and must be addressed @@ -307,7 +306,7 @@ grid points on regions where finer resolution is needed, and (2) high-order numerical techniques. -Several AMR codes, including the {\tt Carpet} driver \cite{CarpetCode:web} +Several AMR codes, including the {\tt Carpet} driver~\cite{CarpetCode:web} included in the Einstein Toolkit, are publicly available. An important task going forward is to facilitate the coupling of existing and future GRMHD codes @@ -462,8 +461,8 @@ The Einstein Toolkit offers two drivers, \codename{PUGH} and {\tt Carpet}. \codename{PUGH} provides domains consisting of a uniform grid with Cartesian topology, and is highly scalable (up to more than -130,000 cores on a Blue Gene/P \cite{Cactuscode:BlueGene:web}.) -{\tt Carpet} \cite{Schnetter:2003rb, Schnetter:2006pg, +130,000 cores on a Blue Gene/P~\cite{Cactuscode:BlueGene:web}.) +{\tt Carpet}~\cite{Schnetter:2003rb, Schnetter:2006pg, CarpetCode:web} provides multi-block methods and adaptive mesh refinement (AMR\@). Multi-block methods cover the domain with a set of (possibly distorted) blocks that exchange boundary information via techniques such as @@ -471,7 +470,7 @@ methods are supported by {\tt Carpet}, the Einstein Toolkit itself does not yet contain any multi-block coordinate systems.} The AMR capabilities -employ the standard Berger-Oliger algorithm \cite{Berger:1984zza} with +employ the standard Berger-Oliger algorithm~\cite{Berger:1984zza} with subcycling in time. AMR implies that resolution in the simulation @@ -497,7 +496,7 @@ interpolation operations are implemented efficiently in {\tt Carpet}, and are applied automatically as specified in the execution schedule, i.e.\ without requiring function calls in user code. -Figure \ref{fig:carpet-details} describes some details of the +Figure~\ref{fig:carpet-details} describes some details of the Berger-Oliger time stepping algorithm. More details are described in \cite{Schnetter:2003rb}. @@ -540,7 +539,7 @@ simulations lies in menial tasks that require no physical or numerical insight. -The Simulation Factory \cite{Thomas:2010aa, SimFactory:web} offers a +The Simulation Factory~\cite{Thomas:2010aa, SimFactory:web} offers a set of abstractions for the tasks necessary to set up and successfully finish numerical simulations based on the {\tt Cactus} framework. These abstractions hide tedious low-level management operations, they @@ -551,7 +550,7 @@ supercomputers to be used in a uniform manner. Using the Simulation Factory, we are able to offer a -tutorial for the Einstein Toolkit \cite{EinsteinToolkit:web} that lets +tutorial for the Einstein Toolkit~\cite{EinsteinToolkit:web} that lets new users download, configure, build, and run full simulations of the coupled Einstein/relativistic hydrodynamics equations on a supercomputer with a few simple commands. Users need no prior @@ -932,10 +931,10 @@ A substantial fraction of the published work on the components of the Einstein toolkit involves the evolution of BH-BH binary systems. The most widely used routine to generate initial data for these is the -\codename{TwoPunctures} code, described originally in \cite{Ansorg:2004ds}, which solves -the binary puncture equations for a pair of BHs \cite{Brandt:1997tf}. +\codename{TwoPunctures} code, described originally in~\cite{Ansorg:2004ds}, which solves +the binary puncture equations for a pair of BHs~\cite{Brandt:1997tf}. To do so, one assumes the extrinsic curvature for each BH corresponds to -the Bowen-York form \cite{Bowen:1980yu}, +the Bowen-York form~\cite{Bowen:1980yu}, \begin{eqnarray} K_{(n)}^{ij}&=&\frac{3}{2r^2}(P^in^j+P^jn^i-(\gamma^{ij}-n^in^jP^kn_k))\nonumber\\ &&+\frac{3}{r^3}(\varepsilon^{ikl}S_kn_ln^j+\varepsilon^{jkl}S_kn_ln^i) @@ -989,7 +988,7 @@ \subsubsection{Lorene-based binary data} The ET contains three routines that can read in publicly available data generated -by the {\tt Lorene} code \cite{Lorene:web,Gourgoulhon:2000nn}, though it does not +by the {\tt Lorene} code~\cite{Lorene:web,Gourgoulhon:2000nn}, though it does not currently include the capability of generating such data from scratch. For a number of reasons, such functionality is not truly required; in particular, {\tt Lorene} is a serial code and there is no time-savings at all to call it as @@ -1027,9 +1026,9 @@ \end{figure} \codename{Meudon\_Bin\_BH} can read in BH-BH binary initial data described -in \cite{Grandclement:2001ed}, while \codename{Meudon\_Bin\_NS} -handles binary NS data from \cite{Gourgoulhon:2000nn}. \codename{Meudon\_Mag\_NS} -may be used to read in magnetized isolated NS data \cite{Lorene:web}. +in~\cite{Grandclement:2001ed}, while \codename{Meudon\_Bin\_NS} +handles binary NS data from~\cite{Gourgoulhon:2000nn}. \codename{Meudon\_Mag\_NS} +may be used to read in magnetized isolated NS data~\cite{Lorene:web}. \subsubsection{TOVSolver} \label{sec:TOVSolver} @@ -1197,7 +1196,7 @@ \\ K_0(x^\mu) & := & 0 \end{eqnarray} -and $\Gamma$-driver shift condition \cite{Alcubierre:2002kk}: +and $\Gamma$-driver shift condition~\cite{Alcubierre:2002kk}: \begin{eqnarray} G(\alpha,\phi,x^\mu) & := & (3/4)\, \alpha^{-2} \\ @@ -1217,7 +1216,7 @@ $\beta^i$ and thus that of the spatial coordinates $x^i$ will be exponentially damped. This damping time scale is set by the gauge parameter $\eta$ (see Eq.~\ref{eq:eta}) which has dimension $1/T$ (inverse time). -As described, e.g., in \cite{Muller:2009jx, Schnetter:2010cz}, this +As described, e.g., in~\cite{Muller:2009jx, Schnetter:2010cz}, this time scale may need to be adapted in different regions of the domain to avoid spurious high-frequency behavior in regions that otherwise evolve only very slowly, e.g., far away from the source. @@ -1270,7 +1269,7 @@ During time evolution, a Sommerfeld-type radiative boundary condition is applied to all components of the evolved BSSN variables as -described in \cite{Alcubierre:2000xu}. The main feature of this boundary +described in~\cite{Alcubierre:2000xu}. The main feature of this boundary condition is that it assumes approximate spherical symmetry of the solution, while applying the actual boundary condition on the boundary of a cubic grid where the face normals are not aligned with the radial @@ -1328,7 +1327,7 @@ this boundary condition leads to stable evolutions if applied sufficiently far from the source. Errors introduced at the boundary (both errors in the geometry and constraint violations) propagate -inwards with the speed of light \cite{Brown:2008sb}. Gauge changes +inwards with the speed of light~\cite{Brown:2008sb}. Gauge changes introduced by the boundary condition, which are physically not observable, propagate faster, with a speed up to $\sqrt{2}$ for the gauge conditions used in \codename{McLachlan}. @@ -1348,7 +1347,7 @@ The primary hydrodynamics evolution routine in the Einstein Toolkit is \codename{GRHydro}, a code derived from the public \codename{Whisky} -code \cite{Baiotti:2004wn,Hawke:2005zw,Baiotti:2010zf,Whisky:web} +code~\cite{Baiotti:2004wn,Hawke:2005zw,Baiotti:2010zf,Whisky:web} designed primarily by researchers at AEI and their collaborators. It includes a high resolution shock capturing (HRSC) scheme to evolve hydrodynamic quantities, with several different reconstruction methods @@ -1400,7 +1399,7 @@ We choose a definition of the 3-velocity that corresponds to the velocity seen by an Eulerian observer at rest in the current spatial -3-hypersurface \cite{}, +3-hypersurface~\cite{}, \begin{equation} v^i = \frac{u^i}{W} + \frac{\beta^i}{\alpha}\,\,, \label{eq:vel} @@ -1480,7 +1479,7 @@ different forms of the slope limiter available. In practice, all try to accomplish the same task of preserving monotonicity and removing the possibility of spuriously creating local extrema. Implemented methods -include minmod, superbee \cite{Roe:1986cb}, and monotonized central \cite{vanLeer:1977aa}. +include minmod, superbee~\cite{Roe:1986cb}, and monotonized central~\cite{vanLeer:1977aa}. The piecewise parabolic method (PPM) is a multi-step method based around a quadratic fit to nearby points interpolated to cell faces @@ -1513,7 +1512,7 @@ in question in space and time. The simplest method implemented is the Harten-Lax-van Leer-Einfeldt -solver \cite{Harten:1983on,Einfeldt:1988og} (HLL or HLLE, depending on the reference), +solver~\cite{Harten:1983on,Einfeldt:1988og} (HLL or HLLE, depending on the reference), which uses a two wave approximation to calculate the evolution along the shock front. With $\xi_-$ and $\xi_+$ the most negative and most positive wave speeds present on either side of the interface, @@ -1546,7 +1545,7 @@ \end{equation} It is these flux terms that are then used to evolve the hydrodynamic quantities. -The Roe solver \cite{Roe:1981ar} involves linearizing the evolution system +The Roe solver~\cite{Roe:1981ar} involves linearizing the evolution system for the hydrodynamic evolution. Eq.~\ref{eq:Riemann}, defining the Jacobian matrix $A\equiv \frac{\partial f}{\partial q}$, and working out the eigenvalues $\lambda^i$ and left and right eigenvectors, @@ -1572,7 +1571,7 @@ \subsubsection{Conservative to primitive conversion} -In order to invert Eqs.~\ref{eq:p2c1} -- \ref{eq:p2c3}, solving for +In order to invert Eqs.~\ref{eq:p2c1}~--~\ref{eq:p2c3}, solving for the primitive variables based on the values of the conservative ones, \codename{GRHydro} uses a 1-dimensional Newton-Raphson approach that solves for a consistent value of the pressure. Defining the (known) @@ -1656,7 +1655,7 @@ is encapsulated in the constant adiabatic index $\Gamma$. This EOS has been used extensively in simulations of NS-NS and BH-NS mergers. -The hybrid EOS, first introduced by \cite{Janka:1993da}, is a 2-piece +The hybrid EOS, first introduced by~\cite{Janka:1993da}, is a 2-piece piecewise polytropic with a thermal component designed for the application in simple models of stellar collapse. At densities below nuclear, a polytropic EOS with $\Gamma = \Gamma_1 \approx 4/3$ is @@ -1878,7 +1877,7 @@ years~\cite{Szabados:2004ql}. Even though only a few rigorous proofs exist that establish the properties of these latter quantities, they have been demonstrated to be surprisingly helpful in numerical simulations -(see, e.g., \cite{Lovelace:2009dg}), and are therefore +(see, e.g.,~\cite{Lovelace:2009dg}), and are therefore an indispensable tool in numerical relativity. \codename{QuasiLocalMeasures} takes as input a horizon surface, or any other surface that the user specifies, like a large coordinate

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 162)
by knarf＠cct.lsu.edu 06 Nov '11

06 Nov '11

User: knarf Date: 2011/11/06 12:30 AM Modified: / ET.tex Log: \ae -> \ae\@ File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +1 -1 =================================================================== --- ET.tex 2011-11-06 05:30:02 UTC (rev 161) +++ ET.tex 2011-11-06 05:30:41 UTC (rev 162) @@ -1873,7 +1873,7 @@ The module \codename{QuasiLocalMeasures} implements the calculation of mass and spin multipoles from the isolated and dynamical horizon formalism~\cite{Dreyer:2002mx, Schnetter:2006yt}, -as well as a number of other proposed formul\ae for quasilocal mass, linear +as well as a number of other proposed formul\ae\@ for quasilocal mass, linear momentum and angular momentum that have been advanced over the years~\cite{Szabados:2004ql}. Even though only a few rigorous proofs exist that establish the properties of these latter quantities, they have

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 161)
by knarf＠cct.lsu.edu 06 Nov '11

06 Nov '11

User: knarf Date: 2011/11/06 12:30 AM Modified: / ET.tex Log: a lot of small details File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +18 -18 =================================================================== --- ET.tex 2011-11-06 05:20:20 UTC (rev 160) +++ ET.tex 2011-11-06 05:30:02 UTC (rev 161) @@ -182,7 +182,7 @@ either the GHG formalism (Caltech/Cornell, LSU/BYU/LIU, and Princeton) or BSSN ``moving puncture'' gauge (or variants thereof; AEI/Sissa, Illinois, Jena, and Tokyo/Kyoto). Nearly all include some form of adaptive mesh -refinement, since unigrid models cannot produce accurate longterm evolutions +refinement, since unigrid models cannot produce accurate long-term evolutions without requiring exorbitant computational resources. Many groups' codes now include GRMHD (used widely for NS-NS mergers, and for BH-NS mergers in \cite{Chawla:2010sw}, and some include microphysical effects as well. @@ -311,7 +311,7 @@ included in the Einstein Toolkit, are publicly available. An important task going forward is to facilitate the coupling of existing and future GRMHD codes - with AMR to avoid underresolving the + with AMR to avoid under-resolving the dynamics in the systems under investigation. AMR methods are often much more complicated than uniformly distributed mesh methods, and require sophisticated algorithms to make use of @@ -409,7 +409,7 @@ Framework~\cite{Cactuscode:web,Goodale:2002a,CactusUsersGuide:web} is an open source, modular, portable programming environment for collaborative HPC computing, primarily developed at Louisiana State University\@. -The generic, parallel {\tt Cactus} computationa toolkit consists of modules providing +The generic, parallel {\tt Cactus} computational toolkit consists of modules providing parallel drivers, coordinates, boundary conditions, interpolators, reduction operators, and efficient I/O in different data formats. Generic interfaces are used, enabling the usage of @@ -529,7 +529,7 @@ Today's supercomputers differ significantly in their hardware configuration, available software, directory structure, -queueing system, queuing policy, and many other user-visible +queuing system, queuing policy, and many other user-visible properties. In addition, the system architectures and user interfaces offered by supercomputers are very different to those offered by laptops or workstations. This makes performing large, @@ -622,7 +622,7 @@ multipatch domains with the Llama\cite{Pollney:2009yz} code; (iii) automatic generation of vectorized code, where the equations are evaluated simultaneously by the processor for two grid points at the same time, and (iv) common -subexpression elimination, and various other optimization strategies. +sub-expression elimination, and various other optimization strategies. Within the Einstein Toolkit, the Einstein evolution thorn McLachlan, as well as the wave extraction thorn WeylScal4, are both generated @@ -870,7 +870,7 @@ module~\cite{Ansorg:2004ds}, commonly used in numerical relativity to generate BH-BH binary initial data, which makes use of the GNU Scientific Library [GSL;~\cite{GSL:web,Galassi:2009}]. -Several modules have also been implemented to read in datafiles generated by +Several modules have also been implemented to read in data files generated by the {\tt Lorene} code~\cite{Lorene:web,Gourgoulhon:2000nn}. Initial data setup is in most cases clearly separated from the @@ -1008,12 +1008,12 @@ rapid falloff at large radii to yield convergent solutions. Around each object, a set of nested spheroidal sub-domains (see Fig.~\ref{fig:Lorene_coordinates}) is constructed extending to cover all of space, with the outermost domain incorporating a compactification to allow -it to extend to spatial infinity. Within each of the nested subdomains, +it to extend to spatial infinity. Within each of the nested sub-domains, fields are decomposed into Chebyshev modes radially and spherical harmonics in the angular directions, with elliptic equation solving reduced to a matrix problem. The nested sub-domains are not required to be perfectly spherical, and indeed one may modify the outer boundaries of each to cover any convex shape. -For NSs, this allows one to map the surface of a particular subdomain +For NSs, this allows one to map the surface of a particular sub-domain to the NS surface, minimizing Gibbs error there. For BHs, excision boundary conditions are imposed at the horizon. To read a field solution describing a given quantity onto a {\tt Cactus}-based grid, one must incorporate the data @@ -1359,7 +1359,7 @@ terms appear in the evolution equations for the conserved variables, they are restricted to appear only inside divergence terms, which are referred to as fluxes, and never in the source terms. By calculating fluxes at cell faces, we may -obtain a consistent description of the intercell values using +obtain a consistent description of the inter-cell values using reconstruction techniques that account for the fact that hydrodynamic variables are not smooth and may not be finite differenced accurately. All other source terms in the evolution equations may contain only the @@ -1516,7 +1516,7 @@ solver \cite{Harten:1983on,Einfeldt:1988og} (HLL or HLLE, depending on the reference), which uses a two wave approximation to calculate the evolution along the shock front. With $\xi_-$ and $\xi_+$ the most negative and -most positive wavespeeds present on either side of the interface, +most positive wave speeds present on either side of the interface, the solution $q(\xi)$ is assumed to take the form \begin{equation} \label{hlle1} @@ -1628,7 +1628,7 @@ An equation of state connecting the primitive state variables is needed to close the system of GR hydrodynamics equations. The module \codename{EOS\_Omni} provides a unified general equation of state -(EOS) interface and backend for simple analytic and complex +(EOS) interface and back-end for simple analytic and complex microphysical EOSs. The polytropic EOS, @@ -1873,7 +1873,7 @@ The module \codename{QuasiLocalMeasures} implements the calculation of mass and spin multipoles from the isolated and dynamical horizon formalism~\cite{Dreyer:2002mx, Schnetter:2006yt}, -as well as a number of other proposed formulae for quasilocal mass, linear +as well as a number of other proposed formul\ae for quasilocal mass, linear momentum and angular momentum that have been advanced over the years~\cite{Szabados:2004ql}. Even though only a few rigorous proofs exist that establish the properties of these latter quantities, they have @@ -2038,7 +2038,7 @@ for $T_{\mu\nu}$. Finally, \codename{ADMAnalysis} calculates a variety of derived spacetime -quantities that are often useful in postprocessing such as the determinant +quantities that are often useful in post-processing such as the determinant of the 3-metric $\det{\gamma}$, the trace of the extrinsic curvature $K$, the 3-Ricci tensor in Cartesian coordinates $\mathcal{R}_{ij}$ and its trace $\mathcal{R}$, as well as the 3-metric and extrinsic curvature converted to @@ -2302,7 +2302,7 @@ \ref{fig:kerr_waves_l4} we can mention that the extracted $\ell =4, m=4$ mode is non-zero due to truncation error, but shows fourth order convergence to zero with resolution (this mode is not present in the initial data and is not -excited during the evolution). Other modes are zero to roundoff due to +excited during the evolution). Other modes are zero to round-off due to symmetries at all resolutions. Since there is non-trivial gravitational wave content in the initial data @@ -2446,7 +2446,7 @@ these were computed to be $4$-th order accurate in this example. The second module, \codename{Multipole}, interpolates the Weyl scalars into spheres with centers and radii specified by -the user, and performs a spherical harmonic multipolar +the user, and performs a spherical harmonic multi-polar mode decomposition on these spherical surfaces. Figure~\ref{fig:tracks_waveform} shows the real and imaginary parts of the ($l=2$, $m=2$) mode for @@ -2657,7 +2657,7 @@ center and a coordinate radius of $r=5\mathrm{M}$ which is about half-way between the center and the surface. The observed convergence rate for most of the simulation time lies between $1.4$ and $1.5$ at the center, and between $1.6$ and -$2$ at $r=5\mathrm{M}$, consistent with the expected data-dependend convergence +$2$ at $r=5\mathrm{M}$, consistent with the expected data-dependent convergence order of the underlying hydrodynamics evolution scheme. \begin{figure} @@ -2695,7 +2695,7 @@ \rho' + K (\rho')^2 = \rho + K_{ID} \rho^2. \label{eqn:collapse_rho_rescaled} \end{equation} -Compared to the initial configuration, this rescaled star posseses a higher +Compared to the initial configuration, this rescaled star possesses a higher central density and lower pressure. This change in $K$ speeds up the collapse and provides a physical trigger for the collapse rather relying on random numerical @@ -2714,7 +2714,7 @@ % radii: 2M,4M,8M,13.6M(!),32M,64M respectively. Changing it to 16M % doesn't really do any good or harm. level is twice that of the surrounding level. In order to resolve the large -density gradients developping during the collapse, two more levels with radii +density gradients developing during the collapse, two more levels with radii $4\,M_\odot$ and $2\,M_\odot$ are present inside of the star. We use the PPM reconstruction method and the HLLE Riemann solver to obtain second order convergent results in smooth regions. Due to the presence of the

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 160)
by knarf＠cct.lsu.edu 06 Nov '11

06 Nov '11

User: knarf Date: 2011/11/06 12:20 AM Modified: / ET.tex /figures/ bbh-boxes.fig, bbh-boxes.pdf Log: a lot of small details File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +93 -99 =================================================================== --- ET.tex 2011-11-06 03:59:34 UTC (rev 159) +++ ET.tex 2011-11-06 05:20:20 UTC (rev 160) @@ -412,7 +412,7 @@ The generic, parallel {\tt Cactus} computationa toolkit consists of modules providing parallel drivers, coordinates, boundary conditions, interpolators, reduction operators, and efficient I/O in different data -formats. Generic interfaces are used, making it possible to use +formats. Generic interfaces are used, enabling the usage of external packages and improved modules which are immediately available to its users. {\tt Cactus} is involved in the NSF Blue Waters consortium for petascale computing, and has funding from NSF SDCI to @@ -439,10 +439,10 @@ group has remained from numerical relativity. The {\tt Cactus} team has traditionally developed and supported a set of core modules for numerical relativity, as part of the \texttt{CactusEinstein} arrangement. Over the -last few years however, the relevance of many of the modules has declined, +years however, the relevance of many of the modules has declined, and more and more of the basic infrastructure for numerical relativity has been provided by open modules distributed by research -groups in the community. +groups within the community. The Einstein Toolkit now collects the widely used parts of CactusEinstein, combined with contributions from the community. @@ -499,13 +499,13 @@ i.e.\ without requiring function calls in user code. Figure \ref{fig:carpet-details} describes some details of the Berger-Oliger time stepping algorithm. More details are described in -\ref{Schnetter:2003rb}. +\cite{Schnetter:2003rb}. \begin{figure} \centering - \includegraphics[width=0.45\textwidth]{figures/carpet-timestepping} - \hfill - \includegraphics[width=0.45\textwidth]{figures/carpet-interpolation} + \includegraphics[width=0.3\textwidth]{figures/carpet-timestepping} + \hspace{3em} + \includegraphics[width=0.3\textwidth]{figures/carpet-interpolation} \caption{Berger-Oliger time stepping details, showing a coarse and a fine grid, with time advancing upwards. \textbf{Left:} Time stepping algorithm. First the coarse grid takes a large time step, then the @@ -522,8 +522,8 @@ used in production on up to several thousand cores. We estimate that, in 2010, about 7,000 core years of computing time (45 million core hours) were used via {\tt Carpet} by more than a dozen research groups -world-wide. To date, more than 90 peer-reviewed publication and more -than 15 student theses are based on {\tt Carpet} \cite{CarpetCode:web}. +world-wide. To date, more than 90 peer-reviewed publications and more +than 15 student theses are based on {\tt Carpet}~\cite{CarpetCode:web}. \subsection{Simulation Factory\pagesdone{1 Erik}} @@ -548,7 +548,7 @@ trail ensuring repeatable and well-documented scientific results. Using these abstractions, most operations are much simplified, many types of potentially disastrous user errors are avoided, allowing different -supercomputers can be used in a uniform manner. +supercomputers to be used in a uniform manner. Using the Simulation Factory, we are able to offer a tutorial for the Einstein Toolkit \cite{EinsteinToolkit:web} that lets @@ -636,7 +636,7 @@ and conventions (see section~\ref{sec:base_modules}). Others provide initial data (see section~\ref{sec:initial_data}), which may be evolved using the different evolution methods described in -section~\ref{sec:evol}. +sections~\ref{sec:Kevol} and~\ref{sec:GRHydro}. Simulations including matter require their own evolution techniques (see section~\ref{sec:GRHydro}) and a description of the matter properties, encoded in equations @@ -651,10 +651,10 @@ Modular designs have proven to be essential for distributed development of complex software systems, and require the use of well-defined interfaces. Low-level interoperability within the Einstein Toolkit is provided by -the {\tt Cactus} infrastructure. One example of this is using one module +the {\tt Cactus} infrastructure. One example of this is the usage of one module from within another, e.g., by calling a function within another thorn -independent of programming language used for both the calling and the -called function. Technical challenges like this can be and are +independent of programming language used for both, the calling and the +called function. Solutions for technical challenges like this can be and are provided by the underlying framework, in this case by {\tt Cactus}. However, certain other standards are very hard or impossible to @@ -669,9 +669,8 @@ The Einstein Toolkit provides modules whose sole purpose is to declare commonly used variables and define their meaning and units. These conditions are not strictly enforced, but instead documented for the -convenience of the user community. Three of these base modules, ADMBase, HydroBase, and TmunuBase, -are described in more detail below, because they declare quantities that might be -defined differently in other simulation codes. +convenience of the user community. Three of these base modules, \codename{ADMBase}, \codename{HydroBase}, and \codename{TmunuBase}, +are described in more detail below. In the following, we assume that the reader is familiar with the basics of numerical relativity and GR hydrodynamics, including the underlying differential geometry and tensor analysis. Detailed @@ -698,8 +697,8 @@ modules using different formalisms. In the $3+1$ approach, 4-dimensional spacetime is foliated into sequences of spacelike 3-dimensional hypersurfaces (slices) connected by timelike normal vectors. The $3+1$ split introduces 4 gauge degrees of freedom, the lapse function $\alpha$ that describes -the advance of proper time with respect to coordinate for a normal -observer\footnote{A normal observer follows a wordline tangent to the +the advance of proper time with respect to coordinate time for a normal +observer\footnote{A normal observer follows a worldline tangent to the unit normal on the 3-hypersurface.} and the shift vector $\beta^i$ that describes how spatial coordinates change from one slice to the next. @@ -770,7 +769,7 @@ function is to store variables which are common to most if not all hydrodynamics codes solving the Euler equations, the so-called primitive variables. These are also the variables which are needed to couple to a -spacetime solver often by analysis thorns as well. As with +spacetime solver, and often by analysis thorns as well. As with ADMBase, the usage of a common set of variables by different hydrodynamics codes creates the possibility of sharing parts of the code, e.g., initial data solvers or analysis routines. @@ -804,11 +803,6 @@ $n^\mu$. \end{itemize} -Note that while this includes definitions for variables used to store information -about magnetic fields, the implementation of an evolution system for magnetic fields -within the Einstein Toolkit is currently still in development and -not yet officially released. - HydroBase also sets up scheduling blocks that organize the main functions that modules of a hydrodynamics code may need. All of those scheduling blocks are optional, but when used they simplify existing codes and make them more interoperable. HydroBase itself does @@ -828,7 +822,7 @@ a central access point for analysis thorns. \subsubsection{TmunuBase} -In the Einstein Toolkit, we typically choose the stress energy tensor $T^{\mu\nu}$ to be that of an ideal relativistic fluid, +In the Einstein Toolkit the stress energy tensor $T^{\mu\nu}$ is often chosen to be that of an ideal relativistic fluid, \begin{equation} T^{\mu\nu} = \rho h u^\mu u^\nu - g^{\mu\nu} P\,\,, \end{equation} @@ -843,7 +837,7 @@ interdependence. The resulting stress-energy tensor can then be used by the spacetime evolution thorn (again without explicit dependence on any matter thorns). When thorn \codename{MoL} is used for time evolution this -provides a high order spacetime-matter coupling. +provides a high-order spacetime-matter coupling. The grid functions provided by \codename{TmunuBase} are: \begin{itemize} @@ -851,7 +845,7 @@ \item The mixed components $T_{0i}$: {\tt eTtx}, {\tt eTty}, {\tt eTtz} \item The spatial components $T_{ij}$: {\tt eTxx}, {\tt eTxy}, {\tt eTxz}, {\tt eTyy}, {\tt eTyz}, {\tt eTzz} \end{itemize} -In addition, the grid scalar {\tt stress\_energy\_state} has the value 1 if storage is on for the stress-energy tensor and 0 if not. +In addition, the grid scalar {\tt stress\_energy\_state} has the value 1 if storage is provided for the stress-energy tensor and 0 if not. Thorn \codename{ADMCoupling} provides a similar (but older) interface between space-time and matter thorns. However, since it is based on an include file @@ -1077,8 +1071,9 @@ handling with some care the potentially singular terms that appear at the origin. To facilitate the construction of stars in more complicated dynamical configurations, -one may also apply a uniform velocity to the NS, though this does not affect -the ODE solution nor the resulting density profile. +one may also apply a uniform velocity to the NS, though this does neither affect +the ODE solution, the resulting density profile nor does it fulfill the spacetime +constraint equations. \subsection{Spacetime Curvature Evolution} \label{sec:Kevol} @@ -1248,8 +1243,8 @@ \subsubsection{Initial Conditions} -Initial conditions from the ADM variables $g_{ij}$, $K_{ij}$, lapse -$\alpha$, and shift $\beta^i$, as provided by the initial data +Initial conditions for the ADM variables $g_{ij}$, $K_{ij}$, lapse +$\alpha$, and shift $\beta^i$, are provided by the initial data discussed in Sec.~\ref{sec:initial_data}. From these the BSSN quantities are calculated via their definition, setting $B^i=0$, and using cubic extrapolation for $\tilde\Gamma^i$ at the outer @@ -1369,8 +1364,7 @@ variables are not smooth and may not be finite differenced accurately. All other source terms in the evolution equations may contain only the hydrodynamic variables themselves as well as the metric variables and -derivatives of the latter, since they must formally be smooth and thus -differentiable using finite differencing techniques. Summarizing +derivatives of the latter. Summarizing these methods briefly, the following stages occur every timestep: \begin{itemize} \item The primitive variables are ``reconstructed'' at cell faces @@ -1380,7 +1374,7 @@ \item A Riemann problem is solved at each cell face using an approximate solver. Currently implemented versions include HLLE (Harten-Lax-van Leer-Einfeldt), Roe, and Marquina solvers. -\item The conserved variables are advanced a timestep, and used to +\item The conserved variables are advanced one timestep, and used to recalculate the new values of the primitive variables. \end{itemize} We discuss the GRHD formalism, the stages within a timestep, and the @@ -1635,7 +1629,7 @@ needed to close the system of GR hydrodynamics equations. The module \codename{EOS\_Omni} provides a unified general equation of state (EOS) interface and backend for simple analytic and complex -microphysical EOS. +microphysical EOSs. The polytropic EOS, \begin{equation} @@ -1724,7 +1718,7 @@ functionality provided by the Einstein Toolkit. In most cases, the analysis modules work on the variables stored in the base modules discussed in Sec.~\ref{sec:base_modules}, \codename{ADMBase}, \codename{TmunuBase}, -and \codename{HydroBase}, to create as portable a tool as possible. +and \codename{HydroBase}, to be as portable as possible. \subsubsection{Horizons} When spacetimes contain a BH, localizing its horizon is necessary @@ -1769,7 +1763,7 @@ the approximate position of the anticipated event horizon to further narrow the region containing the event horizon. -Unfortunately, event horizons can only be found after the full spacetime +However, event horizons can only be found after the full spacetime has been evolved. It is often useful to know the positions and shapes of any BH on a given hypersurface for purposes such as excision, accretion, and local measures of its mass and spin. The @@ -1817,8 +1811,8 @@ The \codename{AHFinderDirect} module~\cite{Thornburg:2003sf} is a faster alternative to \codename{AHFinder}. Its approach is to view -Eq.\ref{eq:ah_theta} as an elliptic PDE for $h(\theta,\phi)$ on $S^2$ -using standard finite differencing methods. Rewriting Eq.~\ref{eq:ah_theta} +eq.~\ref{eq:ah_theta} as an elliptic PDE for $h(\theta,\phi)$ on $S^2$ +using standard finite differencing methods. Rewriting eq.~\ref{eq:ah_theta} in the form \begin{equation} \Theta \equiv \Theta\left(h,\partial_u h,\partial_{uv}h; @@ -1828,7 +1822,8 @@ using a Newton-Raphson method to solve $\bf{J}\cdot\delta h=-\Theta$ where $\bf{J}$ is the Jacobian matrix. The drawback of this method is that it is not guaranteed to give the -outermost marginally trapped surface. +outermost marginally trapped surface. In practice however, this limitation +can be easily overcome by either a good, or multiple initial guesses. \subsubsection{Masses and Momenta} Two distinct measures of mass and momenta are available in relativistic @@ -1857,7 +1852,7 @@ that the integrals of $\tilde{D}^i e^\phi$ and $e^{6\phi} \epsilon_{ij}{}^k x^j \tilde{A}^\ell{}_k$ over the boundaries of the computational domain vanish. The ADM mass and angular momentum -can also be calculated rom the +can also be calculated from the variables stored in the base modules using the \codename{Extract} module, as surface integrals~\cite{Bowen:1980yu} \begin{eqnarray} @@ -1869,7 +1864,7 @@ the domain since these quantities are only properly defined when calculated at infinity. -There are the quasi-local measures of mass and angular momentum. From +There are also the quasi-local measures of mass and angular momentum, from any \ahz{s} found during the spacetime. Both \codename{AHFinderDirect} and \codename{AHFinder} output the corresponding mass derived from the area of the horizon $m_H = @@ -1886,14 +1881,14 @@ (see, e.g., \cite{Lovelace:2009dg}), and are therefore an indispensable tool in numerical relativity. \codename{QuasiLocalMeasures} takes as input a horizon surface, or any -other surface that the user specifies,like a large coordinate +other surface that the user specifies, like a large coordinate sphere, and can calculate useful quantities such as the Weyl or Ricci scalars or the three-volume element of the horizon world tube, -in addition to physical observables such as mass and momenta, +in addition to physical observables such as mass and momenta. Finally, the module \codename{HydroAnalysis} additionally locates the -center of mass as well as the point of maximum rest mass density of a +(coordinate) center of mass as well as the point of maximum rest mass density of a matter field. \subsubsection{Gravitational Waves} @@ -1903,7 +1898,7 @@ data from the various gravitational wave detectors around the globe. The Einstein Toolkit includes modules for extracting gravitational waves via either the Moncrief formalism of a perturbation -on a Schwarzschild background or calculation of the Weyl scalar $\Psi_4$. +on a Schwarzschild background or the calculation of the Weyl scalar $\Psi_4$. The module \codename{Extract} uses the Moncrief formalism~\cite{ Moncrief:1974am} to extract gauge-invariant wavefunctions $Q_{\ell m}^\times$ and $Q_{\ell @@ -1994,6 +1989,34 @@ \end{equation} of a projection onto spin-weighted spherical harmonics ${}_s Y_{\ell m}$. +\todo{CCE} + +\subsubsection{Object tracking} +\label{sec:object-tracking} +We provide a module (\codename{PunctureTracker}) for tracking BH +positions evolved with moving puncture techniques. It can be used +with (\codename{CarpetTracker}) to have the mesh refinement regions follow the +BHs as they move across the grid. The BH position is +stored as the centroid of a spherical surface (even though there is no surface) +provided by \codename{SphericalSurface}. + +Since the punctures only move due to the shift advection terms in +the BSSN equations, the puncture location is evolved very simply as +\begin{equation} + \frac{d x^i}{d t} = -\beta^i, \label{eq:puncturetracking} +\end{equation} +where $x^i$ is the puncture location and $\beta^i$ is the shift. Since the +puncture location usually does not coincide with gridpoints, the shift is +interpolated to the location of the puncture. +Equation~(\ref{eq:puncturetracking}) is implemented with a simple first order +Euler scheme, which seems to be accurate enough for controlling the location +of the mesh refinement hierarchy. + +Another class of objects which often needs to be tracked are neutron stars. +Here is it usually sufficient to locate the position of the maximum density, +and to adapt AMR resolution in these regions accordingly, coupled with the +condition that this location can only move at a specifyable maximum speed. + \subsubsection{Other analysis modules} The remaining analysis capabilities of the Einstein Toolkit span a variety of primarily vacuum-based functions. @@ -2021,37 +2044,6 @@ $\mathcal{R}$, as well as the 3-metric and extrinsic curvature converted to spherical coordinates. - -\subsection{Relativity Tools\pages{3 Peter}} - -\subsubsection*{Object tracking} -\label{sec:object-tracking} -We provide a module (\codename{PunctureTracker}) for tracking BH -positions evolved with moving puncture techniques. It can be used -with (\codename{CarpetTracker}) to have the mesh refinement regions follow the -BHs as they move across the grid. The BH position is -stored as the centroid of a spherical surface (even though there is no surface) -provided by \codename{SphericalSurface}. - -Since the punctures only move due to the shift advection terms in -the BSSN equations, the puncture location is evolved very simply as -\begin{equation} - \frac{d x^i}{d t} = -\beta^i, \label{eq:puncturetracking} -\end{equation} -where $x^i$ is the puncture location and $\beta^i$ is the shift. Since the -puncture location usually does not coincide with gridpoints, the shift is -interpolated to the location of the puncture. -Equation~(\ref{eq:puncturetracking}) is implemented with a simple first order -Euler scheme, which seems to be accurate enough for controlling the location -of the mesh refinement hierarchy. -\todo{ES: I think this paragraph provides too much detail for this paper.} -\todo{ES: Can also track objects via their maximum density or centre - of mass; I believe GRHydro does something like this} -\todo{We mention NS Tracker later, but not here? -Also, should this be incorporated into the Analysis section immediately above, even though these -reside in a different arrangement, since they really are analysis modules?} - - \subsection{Simulation Domain, Symmetries, Boundaries\pages{3 Roland}} \subsubsection{Domains and Coordinates.} {\tt Cactus} distinguishes between @@ -2122,7 +2114,7 @@ In applying symmetries to populate ghost zones, the transformation properties of tensorial quantities (including tensor densities and non-tensors such as Christoffel symbols) are correctly -taken into account, just as they are in the interpolation routines present in {\tt Cactus} +taken into account, just as they are in the interpolation routines present in {\tt Cactus}. Thus, symmetries are handled transparently from the point of view of user modules (see Figure~\ref{fig:faces} for an illustration). @@ -2180,7 +2172,7 @@ \caption{Nested boxes following the individual BHs in binary BH merger simulation (see Section~\ref{sec:bbh-example}), with the location of the individual BHs found by - \codename{PunctureTracker}. The innermost three of the none + \codename{PunctureTracker}. The innermost three of the nine levels of mesh refinement used in this simulation are shown. Notice the use of \codename{RotatingSymmetry180} to reduce the computational domain.} \label{fig:bbh-boxes} @@ -2311,7 +2303,7 @@ is non-zero due to truncation error, but shows fourth order convergence to zero with resolution (this mode is not present in the initial data and is not excited during the evolution). Other modes are zero to roundoff due to -symmetries at all resolution. +symmetries at all resolutions. Since there is non-trivial gravitational wave content in the initial data the mass of the BH changes when evolved. In Figure~\ref{fig:ah_mass} @@ -2368,10 +2360,10 @@ right plot of Figure~\ref{fig:ah_mass_spin} by the fact that the pink (dotted) curve (the high resolution result scaled by a factor of $1.78$ for second order convergence to the resolution of the medium resolution) and the -green (long dashed) curve are on top of each other. The reason that we only -see second order convergence in the spin is due to the fact that thorn -\codename{QuasiLocalMeasures} still have some parts of the algorithm that are -only second order accurate. The increase of about 0.22\% in the mass of the +green (long dashed) curve are on top of each other. The reason for the +second order convergence in the spin lies in the fact that thorn +\codename{QuasiLocalMeasures} uses an algorithm which is +only second order accurate overall. The increase of about 0.22\% in the mass of the BH is caused solely by the increase in the irreducible mass. \subsection{BHB\pages{2 Bruno}} @@ -2472,7 +2464,7 @@ %at this extraction region ($\sim 6.25 \times 10^{-2}$). In order to evaluate the convergence of the numerical -solution, we ran five different simulations with different +solution, we ran five simulations with different resolutions, and focus our analysis on the convergence of the Weyl scalar $\Psi_4$ phase and amplitude. The mesh spacings adopted for the coarser grid in the @@ -2580,6 +2572,7 @@ \end{figure} \subsection{Linear oscillations of TOV stars\pages{2 Frank}} +\label{sec:tov_oscilations} The examples in the previous subsections did not include the evolution of matter within a relativistic spacetime. One interesting test of a coupled matter-spacetime evolution is to measure the eigenfrequencies of a stable TOV @@ -2621,8 +2614,7 @@ an initial spike, produced by the interpolation of the one-dimensional equilibrium solution onto the three-dimensional evolution grid. The remainder of the evolution however, the central density evolution is dominated by continuous excitations coming - from the interaction of the stellar surface with the artificial atmosphere. Shown - are three different resolutions.} + from the interaction of the stellar surface with the artificial atmosphere.} \end{figure} In figure~\ref{fig:tov_mode_spectrum} we show the power spectral density (PSD) @@ -2661,7 +2653,7 @@ surface. Figure~\ref{fig:tov_ham_conv} shows the order of convergence of the Hamiltonian -constraint violation, using the two highest-resolution runs, at the stellar +constraint violation, using the three highest-resolution runs, at the stellar center and a coordinate radius of $r=5\mathrm{M}$ which is about half-way between the center and the surface. The observed convergence rate for most of the simulation time lies between $1.4$ and $1.5$ at the center, and between $1.6$ and @@ -2741,7 +2733,7 @@ disconnecting the evolution in the interior from the outside spacetime.} \end{figure} \begin{figure} - \label{fig:tov_collapse_H_convergence_at0.pdf} + \label{fig:tov_collapse_H_convergence_at0} \includegraphics[width=0.9\textwidth]{examples/collapse/H_convergence_at0} \caption{Convergence factor for the Hamiltonian constraint evaluated at the center of the collapsing star. We plot convergence factors computed using @@ -2798,7 +2790,7 @@ \end{eqnarray} \end{widetext} -In Figure\ref{fig:kasner}, we show the full evolution of the $t=1$ slice +In Figure~\ref{fig:kasner}, we show the full evolution of the $t=1$ slice of spacetime~\ref{eq:kasner}, along with the associated error for a sequence of time resolutions. @@ -2815,7 +2807,7 @@ \section{Future Work\pagesdone{1 Frank}} -In this paper we illustrated the current state of the ``Einstein Toolkit'', +In this paper we illustrated the state of the ``Einstein Toolkit'' release ``Curie'', a collection of freely available and easy to use computational codes for numerical relativity. However, there is room for improvement on both the underlying infrastructure and the included physics. @@ -2831,17 +2823,19 @@ example is the improvement of current wave extraction techniques within the Einstein Toolkit to include Cauchy characteristic wave extraction techniques, as recently studied in~\cite{todo}. The authors of these research codes -recently agreed to make their work available to the whole community within -the Einstein toolkit. This is expected to happen for the second release of -the toolkit in 2011. +agreed to make their work available to the whole community within +the Einstein toolkit, which happened in the recently released version ``Maxwell'', +but which is not described here. A second example for an improvement of an existing method is extending the current implementation of ideal magneto hydrodynamics to the case of non-zero resistivity. Such implementations exist -and are described in the literature~\cite{todo}, but none are provided freely -within the Einstein Toolkit yet. Resistive MHD is important for a number of -astrophysical scenarios, one of which is the merger of two magnetized NSs, -a candidate for short gamma-ray bursts. +and are described in the literature~\cite{todo}, but none have been provided freely +within the Einstein Toolkit until the recently released ``Maxwell'' version. +Resistive MHD is important for a number of astrophysical scenarios, one of +which is the merger of two magnetized NSs, a candidate for short gamma-ray +bursts. +\todo{reword - make clear that we describe Curie} Yet another important goal is to increase the scalability of the {\tt Carpet} AMR infrastructure. It has been shown that good scaling is limited to less than Directory: /figures/ ==================== File [modified]: bbh-boxes.fig Delta lines: +8 -6 =================================================================== --- figures/bbh-boxes.fig 2011-11-06 03:59:34 UTC (rev 159) +++ figures/bbh-boxes.fig 2011-11-06 05:20:20 UTC (rev 160) @@ -8,17 +8,19 @@ 0 1200 2 # polyline -2 1 0 1 0 0 954 0 -1 4.000 0 0 0 0 0 5 - 2848 9757 2848 9757 3856 9757 3856 7384 2848 7384 +2 1 0 1 0 0 954 0 -1 4.000 0 0 0 0 0 4 + 2848 9757 3856 9757 3856 7384 2848 7384 # polyline -2 1 0 1 0 0 952 0 -1 4.000 0 0 0 0 0 5 - 2848 9401 2848 9401 3203 9401 3203 8659 2848 8659 +2 1 0 1 0 0 952 0 -1 4.000 0 0 0 0 0 4 + 2848 9401 3203 9401 3203 8659 2848 8659 # polyline -2 1 0 1 0 0 951 0 -1 4.000 0 0 0 0 0 5 - 2848 8482 2848 8482 3485 8482 3485 7740 2848 7740 +2 1 0 1 0 0 951 0 -1 4.000 0 0 0 0 0 4 + 2848 8482 3485 8482 3485 7740 2848 7740 # polyline 2 1 0 1 0 0 949 0 -1 4.000 0 0 0 0 0 5 2929 8303 3300 8303 3300 7933 2929 7933 2929 8303 2 1 1 1 0 7 50 -1 -1 4.000 0 0 -1 0 0 2 2850 7200 2850 10050 +2 1 1 1 0 7 50 -1 -1 4.000 0 0 -1 0 0 2 + 2850 8575 4425 8575 4 1 0 50 -1 0 12 0.0000 4 135 315 2850 10200 x=0\001 File [modified]: bbh-boxes.pdf Delta lines: +0 -0 =================================================================== (Binary files differ)

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 159)
by knarf＠cct.lsu.edu 05 Nov '11

05 Nov '11

User: knarf Date: 2011/11/05 10:59 PM Modified: / ET.tex Log: tbd author list, fix reference, use uft8 File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +10 -10 =================================================================== --- ET.tex 2011-11-06 03:53:03 UTC (rev 158) +++ ET.tex 2011-11-06 03:59:34 UTC (rev 159) @@ -253,7 +253,7 @@ While the list of studies mentioned in the introduction collectively represent breakthrough simulations that have significantly advanced the modeling of relativistic astrophysical systems, all simulations are presently -missing one or more critical physical ingredients, as well as lacking the +missing one or more critical physical ingredients, as well as the numerical precision to accurately and realistically model the large-scale and small-scale dynamics of their target systems simultaneously. @@ -277,7 +277,7 @@ ideal MHD approximation, which assumes perfect conductivity. Non-ideal GRMHD schemes are just becoming available~(see, e.g.,~\cite{Palenzuela:2008sf,DelZanna:2007pk}), - but yet to be implemented widely in many branches of numerical relativity. + but yet need to be implemented widely in many branches of numerical relativity. \item {\bf Equation of state (EOS), microphysics, and radiation transport}. Most presently published 3D GR(M)HD simulations, with the @@ -286,10 +286,10 @@ (see, e.g., \cite{Sekiguchi:2011zd}), relied on a simple zero-temperature descriptions of NS stellar structure, with many assuming simple polytropic forms. - Such EOS are computationally + Such EOSs are computationally efficient, but are not necessarily a good description for matter in relativistic astrophysical systems. The inclusion of - finite-temperature EOS, derived from the microphysical descriptions of + finite-temperature EOSs, derived from the microphysical descriptions of high-density matter, will lead to qualitatively different and much more astrophysically reliable results (see, e.g.,~\cite{Ott:2006eu}). In addition, most GR(M)HD studies are @@ -353,7 +353,7 @@ In addition, the Einstein Toolkit provides computer scientists an ideal platform to perform state-of-the-art research, which directly benefits research in other areas of science and provides an -immediate application of their research. One of the most prominent +immediate science application. One of the most prominent examples within the Einstein Toolkit is the {\tt Cactus} computational toolkit, a framework developed by computer scientists and now used by researchers is many other fields. @@ -377,15 +377,15 @@ blog requires users to first request a login, but then allows for posting at will. Any user can post comments to entries already on the blog. The community makes heavy use of an issue tracking system -({\tt trac.einsteintoolkit.org}), with submissions also open to everyone. +({\tt trac.einsteintoolkit.org}), with submissions also open to the public. Despite this open design, some actions naturally have to be restricted to a smaller group of maintainers. This is true for, e.g., administrative tasks like the setup and maintenance of the services themselves, or to avoid large amounts of spam. One of the most important tasks of an Einstein Toolkit -Maintainer is to review and apply patches sent by users in order to ensure +maintainer is to review and apply patches sent by users in order to ensure a high software quality level. Every substantial change or addition to -the toolkit has to be reviewed by another Einstein Toolkit Maintainer, +the toolkit has to be reviewed by another Einstein Toolkit maintainer, and is generally open for discussion on the users mailing list. This convention, despite not being technically enforced, works well in practice, and is at the same time promoting active development. @@ -408,8 +408,8 @@ The {\tt Cactus} Framework~\cite{Cactuscode:web,Goodale:2002a,CactusUsersGuide:web} is an open source, modular, portable programming environment for -collaborative HPC computing, primarily developed at LSU\@. {\tt Cactus} has -a generic parallel computational toolkit with modules providing +collaborative HPC computing, primarily developed at Louisiana State University\@. +The generic, parallel {\tt Cactus} computationa toolkit consists of modules providing parallel drivers, coordinates, boundary conditions, interpolators, reduction operators, and efficient I/O in different data formats. Generic interfaces are used, making it possible to use

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 158)
by knarf＠cct.lsu.edu 05 Nov '11

05 Nov '11

User: knarf Date: 2011/11/05 10:53 PM Modified: / ET.tex, plot_defaults.py Log: tbd author list, fix reference, use uft8 File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +16 -26 =================================================================== --- ET.tex 2011-10-28 01:52:58 UTC (rev 157) +++ ET.tex 2011-11-06 03:53:03 UTC (rev 158) @@ -8,7 +8,6 @@ \usepackage{dcolumn} \usepackage{float} \usepackage{graphicx} -\usepackage[latin9]{inputenc} \usepackage{multirow} \usepackage{rotating} \usepackage{subfigure} @@ -18,6 +17,7 @@ \usepackage{wrapfig} \usepackage{multicol} \usepackage{widetext} +\usepackage[utf8]{inputenc} \usepackage[bookmarks, bookmarksopen, bookmarksnumbered]{hyperref} \usepackage[all]{hypcap} @@ -69,32 +69,22 @@ \title[The Einstein Toolkit]{The Einstein Toolkit: A Community Computational Infrastructure for Relativistic Astrophysics} -\author{\textbf{TBD}} - % Short list, not really sorted right now: -%\author{ -%Eloisa Bentivegna, -%Bruno Mundim, -%Christian D. Ott, -%Peter Diener, -%Erik Schnetter, -%Ian Hinder, -%Frank LÃ¶ffler, -%Roland Haas, -%Tanja Bode, +\author{ +Frank LÃ¶ffler, +Eloisa Bentivegna, +Tanja Bode, +Peter Diener, +Joshua Faber, +Roland Haas, +Ian Hinder, +Bruno Mundim, +Christian D. Ott, +Erik Schnetter, +Gabrielle Allen, +Manuela Campanelli, +Pablo Laguna} -% POTENTIAL AUTHORS: M. Alcubierre, G. Allen, M. Ansorg, L. Baiotti, -% E. Bentivegna, S. Bernuzzi, T. Bode, S. Brandt, G. Corvino, R. De -% Pietri, P. Diener, H. Dimmelmeier, Y. El Khamra, J. Faber, T. Font, J. -% Frieben, B. Giacomazzo, T. Goodale, C. Gundlach, R. Haas, I. Hawke, -% S. Hawley, I. Hinder, T. Kellermann, G. Lanfermann, F. L\"{o}ffler, -% J. Masso, M. Miller, P. Montero, B. Mundim, C. Ott, R. Paruchuri, D. Pollney, -% T. Radke, L. Rezzolla, D. Rideout, M. Ripeanu, E. Schnetter, E. -% Seidel, E. L. Seidel, J. Shalf, N. Stergioulas, R. Takahashi, J. -% Thornburg, A. Tonita, P. Walker - - - %\thanks{{}$^{(1)}$ Department of Computer Science, % Louisiana State University, Baton Rouge, LA 70803, USA} %\thanks{{}$^{(2)}$ Department of Physics \& Astronomy, @@ -244,7 +234,7 @@ This success prompted usage of the {\tt Cactus} computational toolkit in other areas, such as ocean forecast models \cite{Djikstra2005} and chemical reaction -simulations \cite{Camarada2001}. At the same time, the growing +simulations \cite{Camarda2001}. At the same time, the growing number of results in numerical relativity increased the need for commonly available utilities such as comparison and analysis tools, typically those specifically designed for astrophysical problems. Including them File [modified]: plot_defaults.py Delta lines: +0 -1 =================================================================== --- plot_defaults.py 2011-10-28 01:52:58 UTC (rev 157) +++ plot_defaults.py 2011-11-06 03:53:03 UTC (rev 158) @@ -39,5 +39,4 @@ M_sol = 1.98892e30 # kg # convertion factors M_to_ms = 1./(1000*M_sol*G/(c*c*c)) -# fix this - what is 7e10? M_to_density = c*c*c*c*c*c / (G*G*G * M_sol*M_sol) # kg/m^3

1 0

[svn:einsteintoolkit] GRHydro/trunk/ (Rev. 298)
by roland.haas＠physics.gatech.edu 04 Nov '11

04 Nov '11

User: rhaas Date: 2011/11/04 01:34 PM Added: /trunk/doc/ constraint_transport.mw Modified: /trunk/ schedule.ccl /trunk/src/ GRHydro_CalcUpdate.F90, GRHydro_Source.F90, GRHydro_SourceM.F90 Log: second iteration of constraint transport * fix some indices * move poison loop to proper spot * compute conserved divergence in track_divB * add Maple worksheet to check constraint transport indices File Changes: Directory: /trunk/doc/ ====================== File [added]: constraint_transport.mw Delta lines: <Unavailable> Directory: /trunk/src/ ====================== File [modified]: GRHydro_CalcUpdate.F90 Delta lines: <Unavailable> File [modified]: GRHydro_Source.F90 Delta lines: <Unavailable> File [modified]: GRHydro_SourceM.F90 Delta lines: <Unavailable> Directory: /trunk/ ================== File [modified]: schedule.ccl Delta lines: <Unavailable>

1 0

[svn:einsteintoolkit] GRHydro/trunk/src/ (Rev. 297)
by tanja.bode＠physics.gatech.edu 04 Nov '11

04 Nov '11

User: tbode Date: 2011/11/04 12:36 PM Modified: /trunk/src/ GRHydro_Con2PrimM.F90 Log: Fix Con2Prim EOS calls in MHD version. File Changes: Directory: /trunk/src/ ====================== File [modified]: GRHydro_Con2PrimM.F90 Delta lines: +35 -32 =================================================================== --- trunk/src/GRHydro_Con2PrimM.F90 2011-11-02 15:04:18 UTC (rev 296) +++ trunk/src/GRHydro_Con2PrimM.F90 2011-11-04 17:36:47 UTC (rev 297) @@ -48,20 +48,22 @@ DECLARE_CCTK_ARGUMENTS DECLARE_CCTK_PARAMETERS + DECLARE_CCTK_FUNCTIONS integer :: i, j, k, itracer, nx, ny, nz - CCTK_REAL :: uxx, uxy, uxz, uyy, uyz, uzz, det, pmin, epsmin + CCTK_REAL :: uxx, uxy, uxz, uyy, uyz, uzz, det, pmin(1), epsmin(1) CCTK_REAL :: b2 CCTK_INT :: epsnegative character(len=100) warnline - CCTK_REAL :: local_min_tracer, local_gam, local_pgam,local_K,sc + CCTK_REAL :: local_min_tracer, local_gam(1), local_pgam,local_K, sc ! begin EOS Omni vars integer :: n,keytemp,anyerr,keyerr(1) - real*8 :: xpress,xtemp,xye,xeps,xrho + real*8 :: xpress(1),xtemp(1),xye(1),xeps(1),xrho(1),one(1)=1.0d0 + n=1;keytemp=0;anyerr=0;keyerr(1)=0 - xpress=0.0d0;xtemp=0.0d0;xye=0.0d0;xeps=0.0d0 + xpress(1)=0.0d0;xtemp(1)=0.0d0;xye(1)=0.0d0;xeps(1)=0.0d0 ! end EOS Omni vars nx = cctk_lsh(1) @@ -75,19 +77,19 @@ end if ! this is a poly call + xrho(1)=GRHydro_rho_min call EOS_Omni_press(GRHydro_polytrope_handle,keytemp,GRHydro_eos_rf_prec,n,& - GRHydro_rho_min,xeps,xtemp,xye,pmin,keyerr,anyerr) + xrho,xeps,xtemp,xye,pmin,keyerr,anyerr) call EOS_Omni_EpsFromPress(GRHydro_polytrope_handle,keytemp,GRHydro_eos_rf_prec,n,& - GRHydro_rho_min,xeps,xtemp,xye,pmin,epsmin,keyerr,anyerr) + xrho,xeps,xtemp,xye,xpress,epsmin,keyerr,anyerr) call EOS_Omni_press(GRHydro_eos_handle,keytemp,GRHydro_eos_rf_prec,n,& - 1.d0,1.d0,xtemp,xye,local_gam,keyerr,anyerr) + one,one,xtemp,xye,local_gam,keyerr,anyerr) local_gam = local_gam+1.d0 - !$OMP PARALLEL DO PRIVATE(i,j,k,itracer,& !$OMP uxx, uxy, uxz, uyy, uyz, uzz, det, epsnegative, & - !$OMP b2,xrho,xeps,xpress,xtemp,local_K,local_pgam,sc,keyerr,anyerr) + !$OMP b2,xrho,xeps,xpress,xtemp,local_K,local_pgam,sc,keyerr,anyerr ) do k = 1, nz do j = 1, ny do i = 1, nx @@ -151,11 +153,11 @@ cycle end if - + if(evolve_temper.eq.0) then - call GRHydro_Con2PrimM_pt(GRHydro_eos_handle, local_gam, dens(i,j,k), & + call GRHydro_Con2PrimM_pt(GRHydro_eos_handle, local_gam(1), dens(i,j,k), & scon(i,j,k,1),scon(i,j,k,2),scon(i,j,k,3), tau(i,j,k), & - Bcons(i,j,k,1), Bcons(i,j,k,2), Bcons(i,j,k,3), rho(i,j,k),& + Bcons(i,j,k,1),Bcons(i,j,k,2),Bcons(i,j,k,3), rho(i,j,k),& vel(i,j,k,1),vel(i,j,k,2),vel(i,j,k,3),eps(i,j,k),press(i,j,k),& Bvec(i,j,k,1), Bvec(i,j,k,2), Bvec(i,j,k,3),b2, w_lorentz(i,j,k),& gxx(i,j,k),gxy(i,j,k),gxz(i,j,k),gyy(i,j,k),gyz(i,j,k),gzz(i,j,k), & @@ -221,12 +223,12 @@ xrho=1.0d0; xtemp=0.0d0; xeps=1.0d0 call EOS_Omni_press(GRHydro_polytrope_handle,keytemp,GRHydro_eos_rf_prec,n,& xrho,xeps,xtemp,xye,xpress,keyerr,anyerr) - local_K = xpress; + local_K = xpress(1); xrho=10.0d0; xeps=1.0d0 call EOS_Omni_press(GRHydro_polytrope_handle,keytemp,GRHydro_eos_rf_prec,n,& xrho,xeps,xtemp,xye,xpress,keyerr,anyerr) - local_pgam=log(xpress/local_K)/log(xrho) + local_pgam=log(xpress(1)/local_K)/log(xrho(1)) sc = local_K*dens(i,j,k) call GRHydro_Con2PrimM_Polytype_pt(GRHydro_eos_handle, local_pgam, dens(i,j,k), & @@ -280,13 +282,14 @@ DECLARE_CCTK_ARGUMENTS DECLARE_CCTK_PARAMETERS + DECLARE_CCTK_FUNCTIONS integer :: i, j, k, itracer, nx, ny, nz CCTK_REAL :: uxxl, uxyl, uxzl, uyyl, uyzl, uzzl,& - uxxr, uxyr, uxzr, uyyr, uyzr, uzzr, pmin, epsmin + uxxr, uxyr, uxzr, uyyr, uyzr, uzzr, pmin(1), epsmin(1) CCTK_REAL :: gxxl,gxyl,gxzl,gyyl,gyzl,gzzl,avg_detl,& gxxr,gxyr,gxzr,gyyr,gyzr,gzzr,avg_detr - CCTK_REAL :: b2minus, b2plus, local_gam, local_pgam,local_K,scminus,scplus + CCTK_REAL :: b2minus, b2plus, local_gam(1), local_pgam,local_K,scminus,scplus CCTK_INT :: epsnegative character(len=100) warnline @@ -294,20 +297,21 @@ ! begin EOS Omni vars integer :: n,keytemp,anyerr,keyerr(1) - real*8 :: xpress,xtemp,xye,xeps,xrho + real*8 :: xpress(1),xtemp(1),xye(1),xeps(1),xrho(1),one(1)=1.0d0 n=1;keytemp=0;anyerr=0;keyerr(1)=0 - xpress=0.0d0;xeps=0.0d0;xtemp=0.0d0;xye=0.0d0 + xpress(1)=0.0d0;xeps(1)=0.0d0;xtemp(1)=0.0d0;xye(1)=0.0d0 ! end EOS Omni vars ! this is a poly call + xrho(1)=GRHydro_rho_min call EOS_Omni_press(GRHydro_polytrope_handle,keytemp,GRHydro_eos_rf_prec,n,& - GRHydro_rho_min,1.0d0,xtemp,xye,pmin,keyerr,anyerr) + xrho,one,xtemp,xye,pmin,keyerr,anyerr) call EOS_Omni_EpsFromPress(GRHydro_polytrope_handle,keytemp,GRHydro_eos_rf_prec,n,& - GRHydro_rho_min,epsmin,xtemp,xye,pmin,epsmin,keyerr,anyerr) + xrho,epsmin,xtemp,xye,pmin,epsmin,keyerr,anyerr) call EOS_Omni_press(GRHydro_eos_handle,keytemp,GRHydro_eos_rf_prec,n,& - 1.d0,1.0d0,xtemp,xye,local_gam,keyerr,anyerr) + one,one,xtemp,xye,local_gam,keyerr,anyerr) local_gam=local_gam+1.0 nx = cctk_lsh(1) @@ -370,7 +374,7 @@ endif - call GRHydro_Con2PrimM_pt(GRHydro_eos_handle, local_gam,densminus(i,j,k), & + call GRHydro_Con2PrimM_pt(GRHydro_eos_handle, local_gam(1),densminus(i,j,k), & sxminus(i,j,k),syminus(i,j,k),szminus(i,j,k), tauminus(i,j,k), & Bconsxminus(i,j,k), Bconsyminus(i,j,k), Bconszminus(i,j,k), rhominus(i,j,k),& velxminus(i,j,k),velyminus(i,j,k),velzminus(i,j,k),epsminus(i,j,k),pressminus(i,j,k),& @@ -386,12 +390,12 @@ xrho=10.0d0 call EOS_Omni_press(GRHydro_polytrope_handle,keytemp,GRHydro_eos_rf_prec,n,& - 1.d0,1.0d0,xtemp,xye,xpress,keyerr,anyerr) - local_K = xpress + one,one,xtemp,xye,xpress,keyerr,anyerr) + local_K = xpress(1) call EOS_Omni_press(GRHydro_polytrope_handle,keytemp,GRHydro_eos_rf_prec,n,& - xrho,1.0d0,xtemp,xye,xpress,keyerr,anyerr) - local_pgam=log(xpress/local_K)/log(xrho) + xrho,one,xtemp,xye,xpress,keyerr,anyerr) + local_pgam=log(xpress(1)/local_K)/log(xrho(1)) scminus = local_K*densminus(i,j,k) call GRHydro_Con2PrimM_Polytype_pt(GRHydro_eos_handle, local_pgam, densminus(i,j,k), & @@ -427,7 +431,7 @@ endif epsnegative = 0 - call GRHydro_Con2PrimM_pt(GRHydro_eos_handle, local_gam, densplus(i,j,k), & + call GRHydro_Con2PrimM_pt(GRHydro_eos_handle, local_gam(1), densplus(i,j,k), & sxplus(i,j,k),syplus(i,j,k),szplus(i,j,k), tauplus(i,j,k),& Bconsxplus(i,j,k), Bconsyplus(i,j,k), Bconszplus(i,j,k), rhoplus(i,j,k),& velxplus(i,j,k),velyplus(i,j,k),velzplus(i,j,k),epsplus(i,j,k),pressplus(i,j,k),& @@ -443,12 +447,12 @@ xrho=10.0d0 call EOS_Omni_press(GRHydro_polytrope_handle,keytemp,GRHydro_eos_rf_prec,n,& - 1.d0,1.0d0,xtemp,xye,xpress,keyerr,anyerr) - local_K = xpress + one,one,xtemp,xye,xpress,keyerr,anyerr) + local_K = xpress(1) call EOS_Omni_press(GRHydro_polytrope_handle,keytemp,GRHydro_eos_rf_prec,n,& - xrho,1.0d0,xtemp,xye,xpress,keyerr,anyerr) - local_pgam=log(xpress/local_K)/log(xrho) + xrho,one,xtemp,xye,xpress,keyerr,anyerr) + local_pgam=log(xpress(1)/local_K)/log(xrho(1)) scplus = local_K*densplus(i,j,k) call GRHydro_Con2PrimM_Polytype_pt(GRHydro_eos_handle, local_pgam, densplus(i,j,k), & @@ -490,7 +494,6 @@ end subroutine Conservative2PrimitiveBoundsM - /*@@ @routine Con2PrimPolytypeM @date Sep 16, 2010

1 0

[svn:einsteintoolkit] GRHydro_InitData/trunk/par/ (Rev. 132)
by bcmsma＠astro.rit.edu 02 Nov '11

02 Nov '11

User: bmundim Date: 2011/11/02 10:50 AM Added: /trunk/par/ balsara1d.par Log: Magnetized diagonal shock parameter file. File Changes: Directory: /trunk/par/ ====================== File [added]: balsara1d.par Delta lines: +114 -0 =================================================================== --- trunk/par/balsara1d.par (rev 0) +++ trunk/par/balsara1d.par 2011-11-02 15:50:12 UTC (rev 132) @@ -0,0 +1,114 @@ +### +ActiveThorns = "time MoL cartgrid3d carpetioascii ioutil Fortran boundary hydrobase grhydro grhydro_initdata nanchecker eos_omni CoordBase LoopControl CarpetLib Carpet CarpetIOHDF5 CarpetReduce spacemask ADMCoupling ADMMacros ADMBASE STATICCONFORMAL TMUNUBASE SymBase localreduce CarpetIOBasic initbase GRHydro_InitData TimerReport" + +NaNChecker::check_every = 1 +NaNChecker::check_vars = "ADMBase::curv ADMBase::metric ADMBase::lapse ADMBase::shift HydroBase::rho HydroBase::eps HydroBase::press HydroBase::vel HydroBase::w_lorentz HydroBase::Bvec" +NaNChecker::action_if_found = "terminate" +#NaNChecker::action_if_found = "abort" +#NaNChecker::action_if_found = "just warn" #"terminate", "just warn", "abort" +#NaNChecker::check_after=0 + +Carpet::output_timers_every = 64 +Carpet::output_timer_tree_every = 64 +Carpet::output_initialise_timer_tree = "yes" +CarpetLib::print_memstats_every = 256 +CarpetLib::memstat_file = "carpetlib-memory-statistics.asc" +TimerReport::out_every = 256 +TimerReport::out_filename = "TimerReport" +#TimerReport::output_all_timers = "yes" +#TimerReport::output_all_timers_together = "yes" +#TimerReport::output_all_timers_readable = "yes" +#TimerReport::before_checkpoint = "yes" +TimerReport::n_top_timers = 40 + + +#This is a hack. ghost_size should be the same as grhydro::grhydro_stencil. + +driver::ghost_size=3 +grhydro::grhydro_stencil=3 + +#time::dtfac = 0.25 +#time::dtfac = 0.8 +time::dtfac = 0.2 + +methodoflines::ODE_Method = "rk2" +methodoflines::MoL_Intermediate_Steps=2 + +#admbase::initial_data="prim2con2prim_test" +#GRHydro_InitData::Bx_init=0.1 +#GRHydro_InitData::By_init=0.12 +#GRHydro_InitData::Bz_init=0.14 +HydroBase::initial_hydro="shocktube" +GRHydro_InitData::shocktube_type="diagshock2D" +GRHydro_InitData::shock_case="Balsara1" + +HydroBase::timelevels=2 +HydroBase::evolution_method="grhydro" +HydroBase::Bvec_evolution_method="grhydro" + +SpaceMask::use_mask="yes" +EOS_Omni::gl_gamma=2.0 +grhydro::track_divB="yes" +grhydro::clean_divergence="yes" +#grhydro::clean_divergence="no" +grhydro::psidcspeed="light speed" +grhydro::kap_dc=1.0 +grhydro::method_type="RSA FV" +grhydro::recon_method="ppm" +#grhydro::recon_method="tvd" +#grhydro::tvd_limiter="vanleerMC" +grhydro::recon_vars="primitive" +grhydro::riemann_solver="HLLE" +#grhydro::bound="flat" +grhydro::bound="none" +grhydro::grhydro_eos_type = "General" +grhydro::grhydro_eos_table="Ideal_Fluid" +grhydro::Grhydro_MaxNumConstrainedVars=13 +grhydro::GRHydro_MaxNumEvolvedVars=10 + +grid::type = "BySpacing" +grid::domain = "full" +#grid::dxyz = 0.01 +#grid::dxyz = 0.000625 +grid::dxyz = 0.0000625 + +driver::global_nx = 150 +driver::global_ny = 150 +driver::global_nz = 9 + +Cactus::terminate="iteration" +#Cactus::terminate="time" +#Cactus::cctk_final_time = 0.02 +#Cactus::cctk_final_time = 0.4 +#cactus::cctk_itlast = 40 +cactus::cctk_itlast = 400 +#cactus::cctk_itlast = 2 + +IO::out_dir = $parfile +#IOBasic::outInfo_every = 1 +#IOBasic::outInfo_vars = "HydroBase::rho" +CarpetIOBasic::outInfo_vars="hydrobase::rho" +CarpetIOBasic::outInfo_every=1 + +#CarpetIOASCII::out1D_criterion = "time" +#CarpetIOASCII::out1D_dt = 0.01 +#CarpetIOASCII::out1D_d=no +#CarpetIOASCII::out1D_vars = "HydroBase::rho HydroBase::press HydroBase::eps HydroBase::vel grhydro::dens grhydro::tau grhydro::scon HydroBase::Bvec" +##CarpetIOASCII::out1D_vars = "HydroBase::rho HydroBase::press HydroBase::eps HydroBase::vel grhydro::psidc grhydro::dens grhydro::tau grhydro::scon HydroBase::Bvec" +##CarpetIOASCII::out1D_vars = "HydroBase::rho HydroBase::press HydroBase::eps HydroBase::vel grhydro::dens grhydro::tau grhydro::scon " + +#CarpetIOHDF5::out_every = 1 +#CarpetIOHDF5::out_vars = "HydroBase::rho HydroBase::press HydroBase::eps HydroBase::vel HydroBase::w_lorentz grhydro::dens grhydro::divB grhydro::tau grhydro::scon HydroBase::Bvec" +##CarpetIOHDF5::out_vars = "HydroBase::rho HydroBase::press HydroBase::eps HydroBase::vel HydroBase::w_lorentz grhydro::psidc grhydro::dens grhydro::divB grhydro::tau grhydro::scon HydroBase::Bvec" +##CarpetIOHDF5::out_vars = "HydroBase::rho HydroBase::press HydroBase::eps HydroBase::vel HydroBase::w_lorentz grhydro::dens grhydro::tau grhydro::scon " + +CarpetIOHDF5::out2D_every = 1 +CarpetIOHDF5::out2D_xy = "yes" +CarpetIOHDF5::out2D_xz = "no" +CarpetIOHDF5::out2D_yz = "no" +CarpetIOHDF5::out2D_xyplane_z = 0.0 +CarpetIOHDF5::out2D_vars = "HydroBase::rho HydroBase::press HydroBase::eps HydroBase::vel HydroBase::w_lorentz grhydro::dens grhydro::divB grhydro::tau grhydro::scon HydroBase::Bvec" +#CarpetIOHDF5::out2D_vars = "HydroBase::rho HydroBase::press HydroBase::eps HydroBase::vel HydroBase::w_lorentz grhydro::psidc grhydro::dens grhydro::divB grhydro::tau grhydro::scon HydroBase::Bvec" +#CarpetIOHDF5::out2D_vars = "HydroBase::rho HydroBase::press HydroBase::eps HydroBase::vel HydroBase::w_lorentz grhydro::dens grhydro::tau grhydro::scon " + +

1 0

Jump to page:

2026

2025

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

Commits