2018/01/31 by Francesco Fambri, Michael Dumbser, Sven Köppel +2 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #A priori and a posteriori #Adaptive mesh refinement #Applied mathematics #Astrophysical Phenomena and Observations #Benchmark (surveying) #Classification of discontinuities #Computational Fluid Dynamics and Aerodynamics #Discontinuous Galerkin method #Finite element method #Finite volume method #Ideal (ethics) #Magnetohydrodynamics #Mathematical analysis #Mathematics #Mechanics #Method of characteristics #Numerical methods for differential equations #Order of accuracy #Partial differential equation #Physics #Spacetime #Total variation diminishing #astro-ph.HE #gr-qc #physics.comp-ph
paper · pdf · doi:10.1093/mnras/sty734
published as Monthly Notices of the Royal Astronomical Society, Volume 477, Issue 4, 2018, Pages 4543-4564 · 23 pages, 14 figures, 6 tables
openalex created_date 2018/01/26 · openalex publication_date 2018/03/23 · arxiv created 2018/05/25 · arxiv updated 2018/05/28 · openalex updated_date 2026/08/05
We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved space–times. In this paper, we assume the background space–time 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 time-stepping. In order to deal with shock waves and other discontinuities, the high-order 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 space–times. 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.