Scalable explicit implementation of anisotropic diffusion with
  Runge-Kutta-Legendre super-time-stepping
  An important ingredient in numerical modelling of high temperature magnetised
astrophysical plasmas is the anisotropic transport of heat along magnetic field
lines from higher to lower temperatures.Magnetohydrodynamics (MHD) typically
involves solving the hyperbolic set of conservation equations along with the
induction equation. Incorporating anisotropic thermal conduction requires to
also treat parabolic terms arising from the diffusion operator. An explicit
treatment of parabolic terms will considerably reduce the simulation time step
due to its dependence on the square of the grid resolution ($\Delta x$) for
stability. Although an implicit scheme relaxes the constraint on stability, it
is difficult to distribute efficiently on a parallel architecture. Treating
parabolic terms with accelerated super-time stepping (STS) methods has been
discussed in literature but these methods suffer from poor accuracy (first
order in time) and also have difficult-to-choose tuneable stability parameters.
In this work we highlight a second order (in time) Runge Kutta Legendre (RKL)
scheme (first described by Meyer et. al. 2012) that is robust, fast and
accurate in treating parabolic terms alongside the hyperbolic conversation
laws. We demonstrate its superiority over the first order super time stepping
schemes with standard tests and astrophysical applications. We also show that
explicit conduction is particularly robust in handling saturated thermal
conduction. Parallel scaling of explicit conduction using RKL scheme is
demonstrated up to more than $10^4$ processors.
