Constrained hyperbolic divergence cleaning in smoothed particle magnetohydrodynamics with variable cleaning speeds
Bate, Matthew R.
Journal of Computational Physics
Reason for embargo
We present an updated constrained hyperbolic/parabolic divergence cleaning algorithm for smoothed particle magnetohydrodynamics (SPMHD) that remains conservative with wave cleaning speeds which vary in space and time. This is accomplished by evolving the quantity ψ/ch instead of ψ. Doing so allows each particle to carry an individual wave cleaning speed, ch, that can evolve in time without needing an explicit prescription for how it should evolve, preventing circumstances which we demonstrate could lead to runaway energy growth related to variable wave cleaning speeds. This modification requires only a minor adjustment to the cleaning equations and is trivial to adopt in existing codes. Finally, we demonstrate that our constrained hyperbolic/parabolic divergence cleaning algorithm, run for a large number of iterations, can reduce the divergence of the magnetic field to an arbitrarily small value, achieving ∇⋅B=0 to machine precision.
TST is supported by ´ a CITA Postdoctoral Research Fellowship. TST and MRB acknowledge support by the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007- 2013 grant agreement no. 339248). DJP is supported by a Future Fellowship (FT130010034) from the Australian Research Council (ARC). This work, and MRB’s visit to Australia in 2014, were part-funded by ARC Discovery Project DP130102078. This research has made use of NASA’s Astrophysics Data System.
This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.
Available online 7 July 2016
Vol. 322, pp. 326 - 344