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A recently developed spectral-element adaptive refinement incompressiblemagnetohydrodynamic (MHD) code [Rosenberg, Fournier, Fischer, Pouquet, J. Comp.Phys. 215, 59-80 (2006)] is applied to simulate the problem of MHD islandcoalescence instability (MICI) in two dimensions. MICI is a fundamental MHDprocess that can produce sharp current layers and subsequent reconnection andheating in a high-Lundquist number plasma such as the solar corona [Ng andBhattacharjee, Phys. Plasmas, 5, 4028 (1998)]. Due to the formation of thincurrent layers, it is highly desirable to use adaptively or statically refinedgrids to resolve them, and to maintain accuracy at the same time. The output ofthe spectral-element static adaptive refinement simulations are compared withsimulations using a finite difference method on the same refinement grids, andboth methods are compared to pseudo-spectral simulations with uniform grids asbaselines. It is shown that with the statically refined grids roughly scalinglinearly with effective resolution, spectral element runs can maintain accuracysignificantly higher than that of the finite difference runs, in some casesachieving close to full spectral accuracy.

the astrophysical journal. supplement series/astrophysical journal. supplement series

A comparison of spectral element and finite difference methods using  statically refined nonconforming grids for the MHD island coalescence  instability problem