dorsal/arxiv
View SchemaAdaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
| Authors | D. Rosenberg, A. Pouquet, P. D. Mininni |
|---|---|
| Categories | |
| ArXiv ID | physics/0703024 |
| URL | https://arxiv.org/abs/physics/0703024 |
| DOI | 10.1088/1367-2630/9/8/304 |
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 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 in the fluid context [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)]; the code allows both statically refined and dynamically refined grids. Tests of the algorithm using analytic solutions are described, and comparisons of the Orszag-Tang 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.
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"abstract": "We examine the effect of accuracy of high-order spectral element methods,\nwith or without adaptive mesh refinement (AMR), in the context of a classical\nconfiguration of magnetic reconnection in two space dimensions, the so-called\nOrszag-Tang vortex made up of a magnetic X-point centered on a stagnation point\nof the velocity. A recently developed spectral-element adaptive refinement\nincompressible magnetohydrodynamic (MHD) code is applied to simulate this\nproblem. The MHD solver is explicit, and uses the Elsasser formulation on\nhigh-order elements. It automatically takes advantage of the adaptive grid\nmechanics that have been described elsewhere in the fluid context [Rosenberg,\nFournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)]; the code allows\nboth statically refined and dynamically refined grids. Tests of the algorithm\nusing analytic solutions are described, and comparisons of the Orszag-Tang\nsolutions with pseudo-spectral computations are performed. We demonstrate for\nmoderate Reynolds numbers that the algorithms using both static and refined\ngrids reproduce the pseudo--spectral solutions quite well. We show that\nlow-order truncation--even with a comparable number of global degrees of\nfreedom--fails to correctly model some strong (sup--norm) quantities in this\nproblem, even though it satisfies adequately the weak (integrated) balance\ndiagnostics.",
"arxiv_id": "physics/0703024",
"authors": [
"D. Rosenberg",
"A. Pouquet",
"P. D. Mininni"
],
"categories": [
"physics.flu-dyn",
"physics.plasm-ph"
],
"doi": "10.1088/1367-2630/9/8/304",
"title": "Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions",
"url": "https://arxiv.org/abs/physics/0703024"
},
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