Stable smoothed particle magnetohydrodynamics in very steep density gradients
This work is a counterpart to LBP2015 where we consider the effect of different
averages on the `average h' SPMHD formalism. We find that there is no substantial difference, except that at low resolutions
the quadratic mean produces erroneous results. This work was presented at the 10th international SPHERIC workshop held in Parma, Italy,
in June 2015
The equations of smoothed particle magnetohydrodynamics (SPMHD), even with the various corrections to instabilities so far proposed,
have been observed to be unstable when a very steep density gradient is necessarily combined with a variable smoothing length formalism.
Here we consider in more detail the modifications made to the SPMHD equations in LBP2015 that resolve this instability by replacing
the smoothing length in the induction and anisotropic force equations with an average smoothing length term. We then explore the choice
of average used and compare the effects on a test ‘cylinder-in-a-box’ problem and the collapse of a magnetised molecular cloud core. We
find that, aside from some benign numerical effects at low resolutions for the quadratic mean, the formalism is robust as to the choice
of average but that in complicated models it is essential to apply the average to both equations; in particular, all four averages
considered exhibit similar conservation properties. This improved formalism allows for arbitrarily small sink particles and field
geometries to be explored, vastly expanding the range of astronomical problems that can be modeled using SPMHD.
Published in the proceedings of the "10th international SPHERIC workshop", Parma, Italy, 16-18 June 2015.
E-print available on the arXiv as arXiv:1506.06595 and
bibliographic data on the ADS.