An unsplit Godunov method for ideal MHD via constrained transport in three dimensions

Thomas A. Gardiner, James McLellan Stone

Research output: Contribution to journalArticlepeer-review

254 Scopus citations


We present a single step, second-order accurate Godunov scheme for ideal MHD which is an extension of the method described in [T.A. Gardiner, J.M. Stone, An unsplit godunov method for ideal MHD via constrained transport, J. Comput. Phys. 205 (2005) 509] to three dimensions. This algorithm combines the corner transport upwind (CTU) method of Colella for multidimensional integration, and the constrained transport (CT) algorithm for preserving the divergence-free constraint on the magnetic field. We describe the calculation of the PPM interface states for 3D ideal MHD which must include multidimensional "MHD source terms" and naturally respect the balance implicit in these terms by the ∇ · B = 0 condition. We compare two different forms for the CTU integration algorithm which require either 6- or 12-solutions of the Riemann problem per cell per time-step, and present a detailed description of the 6-solve algorithm. Finally, we present solutions for test problems to demonstrate the accuracy and robustness of the algorithm.

Original languageEnglish (US)
Pages (from-to)4123-4141
Number of pages19
JournalJournal of Computational Physics
Issue number8
StatePublished - Apr 1 2008

All Science Journal Classification (ASJC) codes

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


  • Compressible flow
  • Magnetohydrodynamics
  • Numerical methods


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