ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics
| Autor: | S. Köppel, Francesco Fambri, Michael Dumbser, Olindo Zanotti, Luciano Rezzolla |
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| Rok vydání: | 2018 |
| Předmět: |
Shocks and discontinuities
FOS: Physical sciences numerical Shock waves Astronomy and Astrophysics Space and Planetary Science [Black hole physics -MHD- relativistic processes Methods] General Relativity and Quantum Cosmology (gr-qc) 010103 numerical & computational mathematics Classification of discontinuities 01 natural sciences General Relativity and Quantum Cosmology Discontinuous Galerkin method Applied mathematics 0101 mathematics High Energy Astrophysical Phenomena (astro-ph.HE) Physics numerical [Methods] Partial differential equation Ideal (set theory) Spacetime Adaptive mesh refinement Black hole physics -MHD- relativistic processes Computational Physics (physics.comp-ph) 010101 applied mathematics Flow (mathematics) Space and Planetary Science Astrophysics - High Energy Astrophysical Phenomena Physics - Computational Physics |
| Zdroj: | Monthly Notices of the Royal Astronomical Society |
| ISSN: | 1365-2966 0035-8711 |
| DOI: | 10.1093/mnras/sty734 |
| Popis: | 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. Comment: 23 pages, 14 figures, 6 tables |
| Databáze: | OpenAIRE |
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