Errata
Clarification of initial condition, boundary value (10-29-2013)
Added an expression of horizontal perturbation of initial temperature by using the spherical harmonics (Section 2.1.4). Added an insulated boundary solution by H. Harder in Wicht et.al. (2009) (Appendix B.1). Thanks to A. Jackson for the suggestion.
Time evolution data fix, addition to documentation (09-27-2013)
The initial temperature was computed incorrectly in the example shown above. The time history data for the both insulated and psedo vacuum cases are now updated to the correct values (the old graph for the insulated case and pseudo vacuum case are available). Thanks for Jean-Luc Guermond for finding this. The benchmark cases have azimuthally symmetrical solutions (m=4) and have symmetry (or anti-symmetry) with respect to the equator. Please report solutions from calculations made with no imposed symmetries. Jackson et. al. revises his manuscript of the paper for the pseudo-vacuum benchmark, and proposes suggested solutions for the benchmark. We follow their suggested solution as the reference solution in the pseudo vacuum case. Thanks for Andrew Jackson for informing this. Reference solution for Pseudo vacuum case
| Old value | New value | |
| Kinetic energy | 40.679 | 40.678 |
| Magnetic energy | 219.40 | 219.39 |
| Local Temperature | 0.4259 | 0.42589 |
| Local velocity | -11.6357 | -11.636 |
| Local magnetic field | 1.404 | 1.4043 |
| Drift frequency | 0.74976 | 0.74990 |
The drift frequency has the largest difference between suggested solution and the old reference solution, but the difference is only 0.02%. Documentation is updated by using the suggested solution by Jackson et. al. and results using the correct initial temperature.
Pseudo-vacuum value fix, addition to documentation (09-17-2013)
The initial condition for the pseudo-vacuum case was computed incorrectly in the example shown above. The above pseudo-vacuum time history and data are now updated to the correct values (the old graph is available here). Thanks for Jean-Luc Guermond for finding this. Documentation for direction of drift and dependence on the direction of initial magnetic field is also added.
Kinetic energy value correction (09-10-2013)
The suggested solution for the kinetic energy in the insulated magnetic boundary case should be 30.773 rather than 30.733 (Tables 2, 4, 5 in the benchmark document). Further details are at http://www.sciencedirect.com/science/article/pii/S0031920108002707