A switch to reduce resistivity in smoothed particle magnetohydrodynamics
  Artificial resistivity is included in Smoothed Particle Magnetohydrodynamics
simulations to capture shocks and discontinuities in the magnetic field. Here
we present a new method for adapting the strength of the applied resistivity so
that shocks are captured but the dissipation of the magnetic field away from
shocks is minimised. Our scheme utilises the gradient of the magnetic field as
a shock indicator, setting {\alpha}_B = h|gradB|/|B|, such that resistivity is
switched on only where strong discontinuities are present. The advantage to
this approach is that the resistivity parameter does not depend on the absolute
field strength. The new switch is benchmarked on a series of shock tube tests
demonstrating its ability to capture shocks correctly. It is compared against a
previous switch proposed by Price & Monaghan (2005), showing that it leads to
lower dissipation of the field, and in particular, that it succeeds at
capturing shocks in the regime where the Alfv\'en speed is much less than the
sound speed (i.e., when the magnetic field is very weak). It is also simpler.
We also demonstrate that our recent constrained divergence cleaning algorithm
has no difficulty with shock tube tests, in contrast to other implementations.
