A finite volume implicit time integration method for solving the equations of ideal magnetohydrodynamics for the hyperbolic divergence cleaning approach

  • Authors:

  • M. S. Yalim;D. Vanden Abeele;A. Lani;T. Quintino;H. Deconinck

  • Affiliations:

  • von Karman Institute for Fluid Dynamics, Department of Aeronautics and Aerospace, Waterloosesteenweg 72, 1640 Sint-Genesius Rode, Belgium;von Karman Institute for Fluid Dynamics, Department of Aeronautics and Aerospace, Waterloosesteenweg 72, 1640 Sint-Genesius Rode, Belgium;von Karman Institute for Fluid Dynamics, Department of Aeronautics and Aerospace, Waterloosesteenweg 72, 1640 Sint-Genesius Rode, Belgium;von Karman Institute for Fluid Dynamics, Department of Aeronautics and Aerospace, Waterloosesteenweg 72, 1640 Sint-Genesius Rode, Belgium;von Karman Institute for Fluid Dynamics, Department of Aeronautics and Aerospace, Waterloosesteenweg 72, 1640 Sint-Genesius Rode, Belgium

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

A finite volume numerical technique is proposed to solve the compressible ideal MHD equations for steady and unsteady problems based on a quasi-Newton implicit time integration strategy. The solenoidal constraint is handled by a hyperbolic divergence cleaning approach allowing its satisfaction up to machine accuracy. The conservation of the magnetic flux is computed in a consistent way using the numerical flux of the finite volume discretization. For the unsteady problem, the time accuracy is obtained by a Newton subiteration at each physical timestep thereby converging the solenoidal constraint to steady state. We perform extensive numerical experiments to validate and demonstrate the capabilities of the proposed numerical technique.