Constrained hyperbolic divergence cleaning in smoothed particle magnetohydrodynamics with variable cleaning speeds

Terrence Tricco, Daniel J. Price, Matthew R. Bate

Research output: Contribution to journalArticleResearchpeer-review

43 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)326-344
Number of pages19
JournalJournal of Computational Physics
Publication statusPublished - 1 Oct 2016


  • Astrophysics
  • Divergence cleaning
  • Magnetic fields
  • MHD
  • Numerical methods
  • Smoothed particle magnetohydrodynamics (SPMHD)

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