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• W2783647117 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." @default.
• W2783647117 created "2018-01-26" @default.
• W2783647117 creator A5001186993 @default.
• W2783647117 creator A5034731703 @default.
• W2783647117 creator A5047765528 @default.
• W2783647117 creator A5051559583 @default.
• W2783647117 creator A5069118120 @default.
• W2783647117 date "2018-03-23" @default.
• W2783647117 modified "2023-10-01" @default.
• W2783647117 title "ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics" @default.
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