Abstract
We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e., we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the highorder DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.
Highlights
Electromagnetism plays an important role in many astrophysical processes such as compact objects and binaries consisting of black holes and neutron stars
We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes
In order to deal with shock waves and other discontinuities, the highorder discontinuous Galerkin (DG) schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, and as accurate as unlimited high-order DG schemes in smooth regions of the flow
Summary
Electromagnetism plays an important role in many astrophysical processes such as compact objects and binaries consisting of black holes and neutron stars. The ADER strategy adopted in this paper, which goes back to Dumbser et al (2008a), applies to general systems of balance laws with conservative fluxes, nonconservative products and stiff or non-stiff algebraic source terms. It is based on a local spacetime discontinuous Galerkin (LSTDG) predictor step, which solves a local Cauchy problem in the small, based on a weak formulation of the partial differential equations in spacetime.
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