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Solving 3D relativistic hydrodynamical problems with weighted essentially nonoscillatory discontinuous Galerkin methods

Bugner, Marcus and Dietrich, Tim and Bernuzzi, Sebastiano and Weyhausen, Andreas and Brügmann, Bernd (2016) Solving 3D relativistic hydrodynamical problems with weighted essentially nonoscillatory discontinuous Galerkin methods. Physical Review D, 94 (8). Art. No. 084004. ISSN 1550-7998. https://resolver.caltech.edu/CaltechAUTHORS:20161003-135251232

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Abstract

Discontinuous Galerkin (DG) methods coupled to weighted essentially nonoscillatory (WENO) algorithms allow high order convergence for smooth problems and for the simulation of discontinuities and shocks. In this work, we investigate WENO-DG algorithms in the context of numerical general relativity, in particular for general relativistic hydrodynamics. We implement the standard WENO method at different orders, a compact (simple) WENO scheme, as well as an alternative subcell evolution algorithm. To evaluate the performance of the different numerical schemes, we study nonrelativistic, special relativistic, and general relativistic test beds. We present the first three-dimensional simulations of general relativistic hydrodynamics, albeit for a fixed spacetime background, within the framework of WENO-DG methods. The most important test bed is a single Tolman-Oppenheimer-Volkoff star in three dimensions, showing that long term stable simulations of single isolated neutron stars can be obtained with WENO-DG methods.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevD.94.084004DOIArticle
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.94.084004PublisherArticle
Additional Information:© 2016 American Physical Society. Received 21 December 2015; published 3 October 2016. It is a pleasure to thank E Harms, D. Hilditch, N. Moldenhauer, M. Pilz, and H. Rüter for helpful discussions. We also thank S. Field and the authors of [57] for sharing numerical data that allowed the direct code comparison in B. This work was supported in part by DFG Grant No. SFB/Transregio 7 “Gravitational Wave Astronomy” and the Graduierten-Akademie Jena. The authors acknowledge the usage of computer resources at the GCS Supercomputer SuperMUC, JUROPA at Jülich Supercomputing Centre, and at the Institute of Theoretical Physics of the University of Jena.
Group:TAPIR
Funders:
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)SFB/Transregio 7
Graduierten-Akademie JenaUNSPECIFIED
Issue or Number:8
Record Number:CaltechAUTHORS:20161003-135251232
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161003-135251232
Official Citation:Solving 3D relativistic hydrodynamical problems with weighted essentially nonoscillatory discontinuous Galerkin methods Marcus Bugner, Tim Dietrich, Sebastiano Bernuzzi, Andreas Weyhausen, and Bernd Brügmann Phys. Rev. D 94, 084004
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:70761
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:03 Oct 2016 21:42
Last Modified:03 Oct 2019 16:01

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