Vector potential remap for 2d MHD

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This report describes an algorithm to remap (rezone) the magnetic vector potential in 2D MHD calculations. This extends a previously described Lagrangian scheme [1] for use with ALE grids, when combined with a suitable remap capability for the hydrodynamic variables. In this scheme, the magnetic field <b>B</b> is a zone quantity derived from the node based vector potential <b>A</b> (<i>B</i><sub>x</sub>, <i>B</i><sub>y</sub>, and <i>A</i><sub>z</sub> in Cartesian geometry, (<i>B</i><sub>z</sub>, <i>B</i><sub>r</sub>, and <i>A</i><sub>(small phi)</sub> in cylindrical geometry). The scheme outlined here is closely related to a flux conserving remap of the magnetic field. Because <b>B</b> is derived from the updated vector potential, however, ... continued below

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Rambo, P W October 13, 1998.

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Description

This report describes an algorithm to remap (rezone) the magnetic vector potential in 2D MHD calculations. This extends a previously described Lagrangian scheme [1] for use with ALE grids, when combined with a suitable remap capability for the hydrodynamic variables. In this scheme, the magnetic field <b>B</b> is a zone quantity derived from the node based vector potential <b>A</b> (<i>B</i><sub>x</sub>, <i>B</i><sub>y</sub>, and <i>A</i><sub>z</sub> in Cartesian geometry, (<i>B</i><sub>z</sub>, <i>B</i><sub>r</sub>, and <i>A</i><sub>(small phi)</sub> in cylindrical geometry). The scheme outlined here is closely related to a flux conserving remap of the magnetic field. Because <b>B</b> is derived from the updated vector potential, however, flux conservation and vanishing divergence are guaranteed; only accuracy is a concern. This is in contrast to schemes based directly on <b>B</b>, which require the additional constraint of preserving zero divergence [2, 3]. Beginning with Cartesian geometry, a straight forward development of the algorithm is first presented; an alternative view is then considered which makes clear the relationship to a flux conservative remapping of the zonal magnetic field. Examples comparing first and second order algorithms are shown, and the issue of energy conservation is discussed. Finally, the generalization to cylindrical geometry is given.

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123 Kilobytes

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  • Other: DE00002463
  • Report No.: UCRL-ID-132123
  • Grant Number: W-7405-Eng-48
  • DOI: 10.2172/2463 | External Link
  • Office of Scientific & Technical Information Report Number: 2463
  • Archival Resource Key: ark:/67531/metadc670137

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  • October 13, 1998

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  • June 29, 2015, 9:42 p.m.

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  • May 6, 2016, 11:09 p.m.

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Rambo, P W. Vector potential remap for 2d MHD, report, October 13, 1998; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc670137/: accessed August 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.