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• W2530159564 abstract "This paper develops $P^K$-based non-central and central Runge-Kutta discontinuous Galerkin (DG) methods with WENO limiter for the one- and two-dimensional special relativistic magnetohydrodynamical (RMHD) equations, $K=1,2,3$. The non-central DG methods are locally divergence-free, while the central DG are exactly divergence-free but have to find two approximate solutions defined on mutually dual meshes. The adaptive WENO limiter first identifies the troubled cells by using a modified TVB minmod function, and then uses the WENO technique to locally reconstruct a new polynomial of degree $(2K+1)$ inside the troubled cells replacing the DG solution by based on the cell average values of the DG solutions in the neighboring cells as well as the original cell averages of the troubled cells. The WENO limiting procedure does not destroy the locally or exactly divergence-free property of magnetic field and is only employed for finite troubled cells so that the computational cost can be as little as possible. Several test problems in one and two dimensions are solved by using our non-central and central Runge-Kutta DG methods with WENO limiter. The numerical results demonstrate that our methods are stable, accurate, and robust in resolving complex wave structures." @default.
• W2530159564 created "2016-10-21" @default.
• W2530159564 creator A5003882350 @default.
• W2530159564 creator A5074411106 @default.
• W2530159564 date "2017-08-01" @default.
• W2530159564 modified "2023-10-18" @default.
• W2530159564 title "Runge–Kutta discontinuous Galerkin methods for the special relativistic magnetohydrodynamics" @default.
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• W2530159564 doi "https://doi.org/10.1016/j.jcp.2017.04.027" @default.
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