Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
Year: 2007
Type: article
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.
Source: New Journal of Physics
Authors: D Rosenberg, A Pouquet, P D Mininni
Institution: NSF National Center for Atmospheric Research
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,610
Funder: National Science Foundation
OpenAlex ID: W1968345469