Bulletin of the American Physical Society
APS April Meeting 2011
Volume 56, Number 4
Saturday–Tuesday, April 30–May 3 2011; Anaheim, California
Session T12: Numerical Relativity: Algorithms and Code Development |
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Sponsoring Units: GGR Chair: Christian Ott, California Institute of Technology Room: Royal CD |
Monday, May 2, 2011 3:30PM - 3:42PM |
T12.00001: Control systems in numerical relativity Mark Scheel Feedback control systems are ubiquitous in various applications encompassing many disciplines. Here we discuss the use of control systems in numerical relativity. For example, control systems can be used to adjust parameters that determine details of the numerical grid or numerical methods, and they can be used to produce efficient smooth-in-time approximations of quantities that are expensive to compute frequently. In particular, we show how numerical relativity simulations can employ control systems to make the numerical grid conform to the dynamically-changing shapes of black hole horizons. [Preview Abstract] |
Monday, May 2, 2011 3:42PM - 3:54PM |
T12.00002: A New AMR Code for Relativistic Magnetohydrodynamics in Dynamical Specetimes: Numerical Method and Code Validation Yuk Tung Liu, Zachariah Etienne, Stuart Shapiro The Illinois relativity group has written and tested a new GRMHD code, which is compatible with adaptive-mesh refinement (AMR) provided by the widely-used Cactus/Carpet infrastructure. Our code solves the Einstein-Maxwell-MHD system of coupled equations in full 3+1 dimensions, evolving the metric via the BSSN formalism and the MHD and magnetic induction equations via a conservative, high-resolution shock-capturing scheme. The induction equations are recast as an evolution equation for the magnetic vector potential. The divergenceless constraint div(B)=0 is enforced by the curl of the vector potential. In simulations with uniform grid spacing, our MHD scheme is numerically equivalent to a commonly used, staggered-mesh constrained-transport scheme. We will present numerical method and code validation tests for both Minkowski and curved spacetimes. The tests include magnetized shocks, nonlinear Alfven waves, cylindrical explosions, cylindrical rotating disks, magnetized Bondi tests, and the collapse of a magnetized rotating star. Some of the more stringent tests involve black holes. We find good agreement between analytic and numerical solutions in these tests, and achieve convergence at the expected order. [Preview Abstract] |
Monday, May 2, 2011 3:54PM - 4:06PM |
T12.00003: Adaptive Mesh Refinement in the Context of Spectral Numerical Evolutions of Binary Black Hole Space-Times Bela Szilagyi Spectral numerical methods are known for giving faster convergence than finite difference methods, when evolving smooth quantities. In binary black hole simulations of the SpEC code this exponential convergence is clearly visible. However, the same exponential dependence of the numerical error on the grid-resolution will also mean that a linear order mismatch between the grid-structure and the actual data will lead to exponential loss of accuracy. In my talk I will show the way the Caltech-Cornell-CITA code deals with this, by use of what we call Spectral AMR. In our algorithm we monitor truncation error estimates in various regions of the grid as the simulation proceeds, and adjust the grid as necessary. [Preview Abstract] |
Monday, May 2, 2011 4:06PM - 4:18PM |
T12.00004: Second-Order Spectral Simulations of Black Hole Binaries Nicholas Taylor Successful spectral simulations of Einstein's equations currently require using a fully first-order formulation, which has the disadvantage of introducing additional constraints and equations. A novel pseudo-spectral penalty method for evolving second-order (in space) hyperbolic equations will be presented. With this method, the penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries as is typical in first-order formulations. The application of this method to the second-order Einstein equations in generalized harmonic form, and especially to the simulation of an equal-mass black hole binary, will be presented and discussed. [Preview Abstract] |
Monday, May 2, 2011 4:18PM - 4:30PM |
T12.00005: Constructing better initial data for compact binary systems Frank L\"offler, Roland Haas, Bruno Mundim, Tanja Bode Some of the most energetic events in astrophysics are believed to be connected to the interaction and merger of compact binaries, consisting of neutron stars and/or black holes. Yet, there are still a lot of uncertainties, especially on binaries involving at least one neutron star. General relativistic effects have to be taken into account when studying these compact objects, complicating analytic studies. Computer simulations of binaries of neutron stars and/or black holes typically solve Einstein's equations of General Relativity and a system of hydrodynamics equations in order to obtain a time sequence. However, the initial data needed to start this sequence also has to satisfy a set of elliptic constraint equations. Solving these equations is difficult for general initial configurations, which is why most solvers are restricted to a very narrow set of parameters. In this talk, we describe one method of generating initial data for compact binary systems, leaving most of the parameters, such as momenta and spins, free to choose. [Preview Abstract] |
Monday, May 2, 2011 4:30PM - 4:42PM |
T12.00006: GenASiS: A full GR-RMHD simulation framework: overview, goals, and preliminary tests Petr Tsatsin, Reuben Budiardja, Christian Cardall, Eirik Endeve, Pedro Marronetti, Anthony Mezzacappa I present an overview of the General Astrophysics Simulation System (GenASiS). GenASiS is currently under development by a collaboration between researchers at the Oak Ridge National Laboratory (ORNL) and Florida Atlantic University (FAU) and features a high-resolution magnetohydrodynamics solver, a full general relativistic description of gravity based on the BSSN formalism, and will feature a two-moment multi-frequency neutrino radiation field evolution. We intend to use GenASiS to study core collapse supernovae, neutron star mergers, and their associated gamma-ray bursts. [Preview Abstract] |
Monday, May 2, 2011 4:42PM - 4:54PM |
T12.00007: Utilizing a GRMHD Code to Determine the Gravitational Radiation from Primordial Turbulence David Garrison In this talk I will show how a GRMHD code can be used to calculate the spectrum of gravitational waves (GWs) produced by turbulence in the early universe. Calculations involving a numerical relativity code should result in a more accurate GW spectrum than other techniques because they allow us to better simulate the conditions of the early universe. Previous calculations of GWs produced by turbulence did not involve compressible fluids or the effects of a dark matter field, a GRMHD simulation can. Also, very little is understood about the turbulent dynamics of a relativistic plasma that may contain supersonic shocks. These can most effectively studied through direct numerical simulation. As a result, the GW spectrum calculated from a GRMHD code may show a much larger deviations from the Kolmogorov Spectrum than has been previously predicted. [Preview Abstract] |
Monday, May 2, 2011 4:54PM - 5:06PM |
T12.00008: Towards a Standardized Characteristic Extraction Tool Maria Babiuc Knowing the precise details of the gravitational wave signature obtained from numerical simulations of binary black hole mergers is a key requirement for meaningful detection and scientific interpretation of the data. However, the waveforms are not easy to be accurately computed. The importance of this problem to the future of gravitational wave astronomy is well recognized. Cauchy-Characteristic Extraction (CCE) is the most precise and refined extraction method available. The CCE technique connects the strong-field Cauchy evolution of the spacetime near the merger to the characteristic evolution to future null infinity where the waveform is extracted in an unambiguous way. Recently, we developed and tested an improved characteristic waveform extraction tool, and demonstrated accuracy and convergence of the numerical error for a binary black hole inspiral and merger. The present version of the extraction module streamlines the start-up of the auxiliary variables by avoiding the use of Taylor expansions. Here, this new method is compared and calibrated in test problems based upon linearized waves. This work offers a practical and efficient way to gain information toward improving the performance of the code and represents a valuable step toward making the extraction tool public. [Preview Abstract] |
Monday, May 2, 2011 5:06PM - 5:18PM |
T12.00009: Gravitational wave extraction in simulations of binary black hole mergers and rotating stellar core collapse Christian Reisswig The accurate modeling of gravitational radiation is a key issue for gravitational wave astronomy. As simulation codes reach higher accuracy, systematic errors inherent in current numerical relativity wave-extraction methods become evident, and may lead to a wrong astrophysical interpretation of the data. Gravitational radiation is properly defined only at future null infinity, scri+, but in practice it is estimated from data calculated at a finite radius. We have used Cauchy-characteristic extraction (CCE) to calculate gravitational radiation at scri+ for the inspiral and merger of two equal mass non-spinning black holes. The implementation is general purpose, and can be applied to calculate the gravitational radiation, at scri+, given data at a finite radius calculated in another computation. This allows us to apply CCE in the context of general relativistic rotating stellar core collapse. We compute the gravitational waves (GWs) emitted in the core bounce phase of three representative models. Using the CCE results as a benchmark, we assess the accuracy of the quadrupole formalism, as well as various curvature-based extraction methods, for the first time applied in simulations of rotating core collapse. [Preview Abstract] |
Monday, May 2, 2011 5:18PM - 5:30PM |
T12.00010: ABSTRACT WITHDRAWN |
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