A high-order shock capturing discontinuous Galerkin–finite difference hybrid method for GRMHD. (6th October 2022)

• Record Type: Journal Article
• Authors: Deppe, Nils; Hébert, François; Kidder, Lawrence E; Teukolsky, Saul A
• Is Part Of: Classical and quantum gravity. Volume 39:Number 19(2022)
• Publication Date: 2022-10-06
• Subjects: discontinuous Galerkin -- finite difference -- GRMHD -- neutron star -- WENO; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/ac8864
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: 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.