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General-relativistic neutron star evolutions with the discontinuous Galerkin method

Hébert, François and Kidder, Lawrence E. and Teukolsky, Saul A. (2018) General-relativistic neutron star evolutions with the discontinuous Galerkin method. Physical Review D, 98 (4). Art. No. 044041. ISSN 2470-0010. doi:10.1103/PhysRevD.98.044041.

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Simulations of relativistic hydrodynamics often need both high accuracy and robust shock-handling properties. The discontinuous Galerkin method combines these features—a high order of convergence in regions where the solution is smooth and shock-capturing properties for regions where it is not—with geometric flexibility and is therefore well suited to solve the partial differential equations describing astrophysical scenarios. We present here evolutions of a general-relativistic neutron star with the discontinuous Galerkin method. In these simulations, we simultaneously evolve the spacetime geometry and the matter on the same computational grid, which we conform to the spherical geometry of the problem. To verify the correctness of our implementation, we perform standard convergence and shock tests. We then show results for evolving, in three dimensions, a Kerr black hole; a neutron star in the Cowling approximation (holding the spacetime metric fixed); and, finally, a neutron star where the spacetime and matter are both dynamical. The evolutions show long-term stability, good accuracy, and an improved rate of convergence versus a comparable-resolution finite-volume method.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Kidder, Lawrence E.0000-0001-5392-7342
Teukolsky, Saul A.0000-0001-9765-4526
Additional Information:© 2018 American Physical Society. Received 5 April 2018; published 27 August 2018. We thank Andy Bohn, Mike Boyle, Nils Deppe, Matt Duez, Francois Foucart, Jan Hesthaven, Curran Muhlberger, and Will Throwe for many helpful conversations through the course of this work. We gratefully acknowledge support for this research from the Sherman Fairchild Foundation; from NSF Grants No. PHY-1606654 and No. AST-1333129 at Cornell; and from NSF Grants No. PHY-1404569, No. PHY-1708212, and No. PHY-1708213 at Caltech. F. H. acknowledges support by the NSF Graduate Research Fellowship under Grant No. DGE-1144153. Computations were performed at Caltech on the Zwicky cluster, which is supported by the Sherman Fairchild Foundation and by NSF Grant No. PHY-0960291, and on the Wheeler cluster, which is supported by the Sherman Fairchild Foundation.
Group:Astronomy Department
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
NSF Graduate Research FellowshipDGE-1144153
Issue or Number:4
Record Number:CaltechAUTHORS:20180606-164721712
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86873
Deposited By: George Porter
Deposited On:07 Jun 2018 14:25
Last Modified:15 Nov 2021 20:43

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