Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions

AMS Citation:
Rosenberg, D. L., A. Pouquet, and P. D. Mininni, 2007: Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions. New Journal of Physics, 9, 20 pp, doi:10.1088/1367-2630/9/8/304.
Date:2007-08-01
Resource Type:article
Title:Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
Abstract: We examine the effect of accuracy of high-order spectral element methods, with or without adaptive mesh refinement (AMR), in the context of a classical configuration of magnetic reconnection in two space dimensions, the so-called Orszag-Tang (OT) vortex made up of a magnetic X-point centred on a stagnation point of the velocity. A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code is applied to simulate this problem. The MHD solver is explicit, and uses the Elsässer formulation on high-order elements. It automatically takes advantage of the adaptive grid mechanics that have been described elsewhere in the fluid context (Rosenberg et al 2006 J. Comput. Phys. 215 59–80); the code allows both statically refined and dynamically refined grids. Tests of the algorithm using analytic solutions are described, and comparisons of the OT solutions with pseudo-spectral computations are performed. We demonstrate for moderate Reynolds numbers that the algorithms using both static and refined grids reproduce the pseudo-spectral solutions quite well. We show that low-order truncation--even with a comparable number of global degrees of freedom--fails to correctly model some strong (sup-norm) quantities in this problem, even though it satisfies adequately the weak (integrated) balance diagnostics.
Peer Review:Refereed
Copyright Information:Copyright 2007 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
OpenSky citable URL: ark:/85065/d7gq6xzq
Publisher's Version: 10.1088/1367-2630/9/8/304
Author(s):
  • Duane Rosenberg - NCAR/UCAR
  • Annick Pouquet - NCAR/UCAR
  • Pablo Mininni - NCAR/UCAR
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