A fully implicit numerical method for single-fluid resistive magnetohydrodynamics

Daniel R. Reynolds*, Ravi Samtaney, Carol S. Woodward

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


We present a nonlinearly implicit, conservative numerical method for integration of the single-fluid resistive MHD equations. The method uses a high-order spatial discretization that preserves the solenoidal property of the magnetic field. The fully coupled PDE system is solved implicitly in time, providing for increased interaction between physical processes as well as additional stability over explicit-time methods. A high-order adaptive time integration is employed, which in many cases enables time steps ranging from one to two orders of magnitude larger than those constrained by the explicit CFL condition. We apply the solution method to illustrative examples relevant to stiff magnetic fusion processes which challenge the efficiency of explicit methods. We provide computational evidence showing that for such problems the method is comparably accurate with explicit-time simulations, while providing a significant runtime improvement due to its increased temporal stability.

Original languageEnglish (US)
Pages (from-to)144-162
Number of pages19
JournalJournal of Computational Physics
Issue number1
StatePublished - Nov 20 2006
Externally publishedYes


  • Implicit couplings
  • Newton-Krylov
  • Resistive magnetohydrodynamics

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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