2013/12/30 by Olindo Zanotti, Michael Dumbser, Zanotti, Olindo +1 · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Astrophysical Phenomena (astro-ph.HE) #Ionosphere and magnetosphere dynamics #Magnetic confinement fusion research #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1312.7784
openalex publication_date 2013/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a high order one-step ADER-WENO finite volume scheme with\nspace-time adaptive mesh refinement (AMR) for the solution of the special\nrelativistic hydrodynamic and magnetohydrodynamic equations. By adopting a\nlocal discontinuous Galerkin predictor method, a high order one-step time\ndiscretization is obtained, with no need for Runge--Kutta sub-steps. This turns\nout to be particularly advantageous in combination with space-time adaptive\nmesh refinement, which has been implemented following a "cell-by-cell"\napproach. As in existing second order AMR methods, also the present higher\norder AMR algorithm features time-accurate local time stepping (LTS), where\ngrids on different spatial refinement levels are allowed to use different time\nsteps. We also compare two different Riemann solvers for the computation of the\nnumerical fluxes at the cell interfaces. The new scheme has been validated over\na sample of numerical test problems in one, two and three spatial dimensions,\nexploring its ability in resolving the propagation of relativistic\nhydrodynamical and magnetohydrodynamical waves in different physical regimes.\nThe astrophysical relevance of the new code for the study of the\nRichtmyer--Meshkov instability is briefly discussed in view of future\napplications.\n