Adaptive Mesh Refinement With Spectral Accuracy for Magnetohydrodynamics in Two Space Dimensions

Details Adaptive Mesh Refinement With Spectral Accuracy for Magnetohydrodynamics in Two Space Dimensions Adaptive Mesh Refinement With Spectral Accuracy for Magnetohydrodynamics in Two Space Dimensions

Dec 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006agufmsh23b0365r&link_type=abstract

American Geophysical Union, Fall Meeting 2006, abstract #SH23B-0365

Statistics

Computation

4445 Nonlinear Differential Equations, 4490 Turbulence (3379, 4568, 7863), 7526 Magnetic Reconnection (2723, 7835)

Scientific paper

We examine the effect of accuracy of high-order adaptive mesh refinement (AMR) in the context of a classical configuration of magnetic reconnection in two space dimensions, the so-called Orszag-Tang vortex made up of a magnetic X-point centered 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 Elsasser formulation on high-order elements. It automatically takes advantage of the adaptive grid mechanics that have been described elsewhere [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)] in the fluid context, allowing both statically refined and dynamically refined grids. Comparisons with pseudo-spectral computations are performed. Refinement and coarsening criteria are examined, and several tests are described. We show that low-order truncation--even with a comparable number of global degrees of freedom--fails to correctly model some strong (inf-norm) quantities in this problem, even though it satisfies adequately the weak (integrated) balance diagnostics.

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