A Caltech Library Service

A high-order shock capturing discontinuous Galerkin-finite difference hybrid method for GRMHD

Deppe, Nils and Hébert, François and Kidder, Lawrence E. and Teukolsky, Saul A. (2022) A high-order shock capturing discontinuous Galerkin-finite difference hybrid method for GRMHD. Classical and Quantum Gravity, 39 (19). Art. No. 195001. ISSN 0264-9381. doi:10.1088/1361-6382/ac8864.

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item:


We present a discontinuous Galerkin (DG)–finite difference (FD) hybrid scheme that allows high-order shock capturing with the DG method for general relativistic magnetohydrodynamics. The hybrid method is conceptually quite simple. An unlimited DG candidate solution is computed for the next time step. If the candidate solution is inadmissible, the time step is retaken using robust FD methods. Because of its a posteriori nature, the hybrid scheme inherits the best properties of both methods. It is high-order with exponential convergence in smooth regions, while robustly handling discontinuities. We give a detailed description of how we transfer the solution between the DG and FD solvers, and the troubled-cell indicators necessary to robustly handle slow-moving discontinuities and simulate magnetized neutron stars. We demonstrate the efficacy of the proposed method using a suite of standard and very challenging 1D, 2D, and 3D relativistic magnetohydrodynamics test problems. The hybrid scheme is designed from the ground up to efficiently simulate astrophysical problems such as the inspiral, coalescence, and merger of two neutron stars.

Item Type:Article
Related URLs:
URLURL TypeDescription
Deppe, Nils0000-0003-4557-4115
Hébert, François0000-0001-9009-6955
Kidder, Lawrence E.0000-0001-5392-7342
Teukolsky, Saul A.0000-0001-9765-4526
Additional Information:Charm++/Converse [85] was developed by the Parallel Programming Laboratory in the Department of Computer Science at the University of Illinois at Urbana-Champaign. The figures in this article were produced with matplotlib [86, 87], TikZ [88] and ParaView [89, 90]. Computations were performed with the Wheeler cluster at Caltech. This work was supported in part by the Sherman Fairchild Foundation and by NSF Grant Nos. PHY-2011961, PHY-2011968, and OAC-1931266 at Caltech, and NSF Grant Nos. PHY-1912081 and OAC-1931280 at Cornell.
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Issue or Number:19
Record Number:CaltechAUTHORS:20220909-232652000
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:116863
Deposited By: Donna Wrublewski
Deposited On:08 Dec 2022 23:55
Last Modified:08 Dec 2022 23:55

Repository Staff Only: item control page