Simulating magnetized neutron stars with discontinuous Galerkin methods
arXiv:2109.12033 · doi:10.1103/PhysRevD.105.123031
Abstract
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/ 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 TOV 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.
arXiv commentmatches published version. 21 pages, 12 figures. Added KH instability, TOV runs with classical limiters. arXiv admin note: text overlap with arXiv:2109.11645
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