Mimetic Methods for Lagrangian Relaxation of Magnetic Fields
Abstract
We present a new code that performs a relaxation of a magnetic field towards a forcefree state (Beltrami field) using a Lagrangian numerical scheme. Beltrami fields are of interest for the dynamics of many technical and astrophysical plasmas as they are the lowest energy states that the magnetic field can reach. The numerical method strictly preserves the magnetic flux and the topology of magnetic field lines. In contrast to other implementations we use mimetic operators for the spatial derivatives in order to improve accuracy for high distortions of the grid. Compared with schemes using direct derivatives we find that the final state of the simulation approximates a forcefree state with a significantly higher accuracy. We implement the scheme in a code which runs on graphical processing units (GPU), which leads to an enhanced computing speed compared to previous relaxation codes.
 Publication:

SIAM Journal on Scientific Computing
 Pub Date:
 January 2014
 DOI:
 10.1137/140967404
 arXiv:
 arXiv:1405.0942
 Bibcode:
 2014SJSC...36B.952C
 Keywords:

 Physics  Plasma Physics;
 Astrophysics  Solar and Stellar Astrophysics;
 Physics  Computational Physics;
 65D25;
 47F05;
 65M06;
 68W40;
 76W05;
 8508;
 85A30
 EPrint:
 16 pages, 8 figures, submitted to SIAM Journal on Scientific Computing