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

Abstract

We present a discontinuous Galerkin-finite-difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics. The hybrid method is conceptually quite simple. An unlimited discontinuous Galerkin candidate solution is computed for the next time step. If the candidate solution is inadmissible, the time step is retaken using robust finite-difference 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 discontinuous Galerkin and finite-difference 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.

Matches published version (sorry for delay reposting). 45 pages, 14 figures. Showed 2 more Riemann problems, added rotating NS test

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Cited by in corpus (6)

• The new discontinuous Galerkin methods based numerical relativity program Nmesh
• Simulating binary black hole mergers using discontinuous Galerkin methods
• Simulating neutron stars with a flexible enthalpy-based equation of state parametrization in SpECTRE
• General relativistic force-free electrodynamics with a discontinuous Galerkin-finite difference hybrid method
• High-order discontinuous Galerkin schemes with subcell finite volume limiter and adaptive mesh refinement for a monolithic first-order BSSNOK formulation of the Einstein-Euler equations
• Neutron star evolution by combining discontinuous Galerkin and finite volume methods