A constrained transport scheme for MHD on unstructured static and moving meshes
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Vogelsberger_A constrained.pdf
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Author(s)
Mocz, Philip
Hernquist, L.
Vogelsberger, Mark
Date Issued
June 2014
Journal
Monthly Notices of the Royal Astronomical Society
Publisher
Oxford University Press
Citation
Mocz, P., M. Vogelsberger, and L. Hernquist. “A Constrained Transport Scheme for MHD on Unstructured Static and Moving Meshes.” Monthly Notices of the Royal Astronomical Society 442, no. 1 (June 2, 2014): 43–55.
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Author's final manuscript
Abstract
Magnetic fields play an important role in many astrophysical systems and a detailed understanding of their impact on the gas dynamics requires robust numerical simulations. Here we present a new method to evolve the ideal magnetohydrodynamic (MHD) equations on unstructured static and moving meshes that preserves the magnetic field divergence-free constraint to machine precision. The method overcomes the major problems of using a cleaning scheme on the magnetic fields instead, which is non-conservative, not fully Galilean invariant, does not eliminate divergence errors completely, and may produce incorrect jumps across shocks. Our new method is a generalization of the constrained transport (CT) algorithm used to enforce the ∇ · B = 0 condition on fixed Cartesian grids. Preserving ∇ · B = 0 at the discretized level is necessary to maintain the orthogonality between the Lorentz force and B. The possibility of performing CT on a moving mesh provides several advantages over static mesh methods due to the quasi-Lagrangian nature of the former (i.e. the mesh generating points move with the flow), such as making the simulation automatically adaptive and significantly reducing advection errors. Our method preserves magnetic fields and fluid quantities in pure advection exactly.
MIT Department
Massachusetts Institute of Technology. Department of Physics
MIT Kavli Institute for Astrophysics and Space Research
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DOI of Published Version
https://doi.org/10.1093/mnras/stu865
