Discontinuous Galerkin methods are popular because they can achieve high order where the solution is smooth, because they can capture shocks while needing only nearest-neighbor communication, and because they are relatively easy to formulate on complex meshes. We perform a detailed comparison of various limiting strategies presented in the literature applied to the equations of general relativistic magnetohydrodynamics. We compare the standard minmod /Λ ΠN limiter, the hierarchical limiter of Krivodonova, the simple WENO limiter, the HWENO limiter, and a discontinuous Galerkin-finite-difference hybrid method. The ultimate goal is to understand what limiting strategies are able to robustly simulate magnetized Tolman-Oppenheimer-Volkoff stars without any fine-tuning of parameters. Among the limiters explored here, the only limiting strategy we can endorse is a discontinuous Galerkin-finite-difference hybrid method.
Physical Review D
- Pub Date:
- June 2022
- General Relativity and Quantum Cosmology;
- Astrophysics - High Energy Astrophysical Phenomena
- matches published version. 21 pages, 12 figures. Added KH instability, TOV runs with classical limiters. arXiv admin note: text overlap with arXiv:2109.11645