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Formulation of discontinuous Galerkin methods for relativistic astrophysics

Teukolsky, Saul A. (2016) Formulation of discontinuous Galerkin methods for relativistic astrophysics. Journal of Computational Physics, 312 . pp. 333-356. ISSN 0021-9991. http://resolver.caltech.edu/CaltechAUTHORS:20160408-083733301

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Abstract

The DG algorithm is a powerful method for solving pdes, especially for evolution equations in conservation form. Since the algorithm involves integration over volume elements, it is not immediately obvious that it will generalize easily to arbitrary time-dependent curved spacetimes. We show how to formulate the algorithm in such spacetimes for applications in relativistic astrophysics. We also show how to formulate the algorithm for equations in non-conservative form, such as Einstein's field equations themselves. We find two computationally distinct formulations in both cases, one of which has seldom been used before for flat space in curvilinear coordinates but which may be more efficient. We also give a new derivation of the ALE algorithm (Arbitrary Lagrangian–Eulerian) using 4-vector methods that is much simpler than the usual derivation and explains why the method preserves the conservation form of the equations. The various formulations are explored with some simple numerical experiments that also investigate the effect of the metric identities on the results. The results of this paper may also be of interest to practitioners of DG working with curvilinear elements in flat space.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.jcp.2016.02.031DOIArticle
http://www.sciencedirect.com/science/article/pii/S0021999116000954PublisherArticle
https://arxiv.org/abs/1510.01190arXivDiscussion Paper
Additional Information:© 2016 Elsevier Inc. Received 27 July 2015; Received in revised form 10 December 2015; Accepted 11 February 2016; Available online 17 February 2016. I thank François Hébert for helpful discussions. I am grateful for the hospitality of TAPIR and the Walter Burke Institute for Theoretical Physics at Caltech where part of this work was carried out. This work was supported in part by NSF Grants PHY-1306125 and AST-1333129 at Cornell University, and by a grant from the Sherman Fairchild Foundation.
Group:TAPIR, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
NSFPHY-1306125
NSFAST-1333129
Sherman Fairchild FoundationUNSPECIFIED
Subject Keywords:Discontinuous Galerkin; Hydrodynamics; Magnetohydrodynamics; Einstein's equations; Moving mesh; Arbitrary Lagrangian–Eulerian (ALE); Metric identities; Geometric conservation law
Record Number:CaltechAUTHORS:20160408-083733301
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160408-083733301
Official Citation:Saul A. Teukolsky, Formulation of discontinuous Galerkin methods for relativistic astrophysics, Journal of Computational Physics, Volume 312, 1 May 2016, Pages 333-356, ISSN 0021-9991, http://dx.doi.org/10.1016/j.jcp.2016.02.031.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66012
Collection:CaltechAUTHORS
Deposited By: Melissa Ray
Deposited On:08 Apr 2016 20:08
Last Modified:08 Apr 2016 20:08

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