Abstract
We present SphericalNR, a new framework for the publicly available Einstein Toolkit that numerically solves the Einstein field equations coupled to the equations of general relativistic magnetohydrodynamic (GRMHD) in a 3+1 split of spacetime in spherical coordinates without symmetry assumptions. The spacetime evolution is performed using reference-metric versions of either the Baumgarte-Shapiro-Shibata-Nakamura equations or the fully covariant and conformal Z4 system with constraint damping. We have developed a reference-metric version of the Valencia formulation of GRMHD with a vector potential method, guaranteeing the absence of magnetic monopoles during the evolution. In our framework, every dynamical field (both spacetime and matter) is evolved using its components in an orthonormal basis with respect to the spherical reference metric. Furthermore, all geometric information about the spherical coordinate system is encoded in source terms appearing in the evolution equations. This allows for the straightforward extension of Cartesian high-resolution shock-capturing finite volume codes to use spherical coordinates with our framework. To this end, we have adapted GRHydro, a Cartesian finite volume GRMHD code already available in the Einstein Toolkit, to use spherical coordinates. We present the full evolution equations of the framework, as well as details of its implementation in the Einstein Toolkit. We validate SphericalNR by demonstrating it passes a variety of challenging code tests in static and dynamical spacetimes.
| Original language | English |
|---|---|
| Article number | 104007 |
| Journal | Physical Review D |
| Volume | 101 |
| Issue number | 10 |
| DOIs | |
| State | Published - May 15 2020 |
Funding
The authors would like to thank the anonymous referee for useful comments and suggestions. We furthermore would like to thank Eirik Endeve for a careful reading of the paper, as well as Miguel Á. Aloy, Mark J. Avara, Dennis B. Bowen, Pablo Cerdá-Durán, Isabel Cordero-Carrión, José A. Font, Roland Haas, David Hilditch, José M. Ibáñez, Kenta Kiuchi, Oleg Korobkin, Jens Mahlmann, Jonah M. Miller, Martin Obergaulinger, Scott C. Noble, David Radice, Ian Ruchlin, Erik Schnetter, and Masaru Shibata for useful discussions. We gratefully acknowledge the National Science Foundation (NSF) for financial support from Grants No. OAC-1550436, No. AST-1516150, No. PHY-1607520, No. PHY-1305730, No. PHY-1707946, and No. PHY-1726215 to Rochester Institute of Technology (RIT); Grant No. PHY-1707526 to Bowdoin College; as well as Grants No. OIA-1458952 and No. PHY-1806596 to West Virginia University (WVU). This work was also supported by NASA Grant No. ISFM-80NSSC18K0538 and No. TCAN-80NSSC18K1488, as well as through sabbatical support from the Simons Foundation (Grant No. 561147 to T. W. B.). V. M. was partially supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy (DOE) Office of Science and the National Nuclear Security Administration. Work at Oak Ridge National Laboratory is supported under contract DE-AC05-00OR22725 with the U.S. Department of Energy. V. M. also acknowledges partial support from the Ministry of Economy and Competitiveness (MINECO) through Grant No AYA2015-66899-C2-1-P and RIT for the FGWA SIRA initiative. This work used the Extreme Science and Engineering Discovery Environment (XSEDE) [allocation TG-PHY060027N], which is supported by NSF Grant No. ACI-1548562, and the BlueSky and Green Prairies Clusters at RIT, which are supported by NSF Grants No. AST-1028087, No. PHY-0722703, No. PHY-1229173, and No. PHY-1726215. Funding for computer equipment to support the development of SENR/NRPy+ was provided in part by NSF EPSCoR Grant OIA-1458952 to West Virginia University. Computational resources were also provided by the Blue Waters sustained-petascale computing NSF project OAC-1516125. All figures in this paper were created using Matplotlib for which we have used the scidata library to import Carpet data.