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07 February 2025
 
  » arxiv » astro-ph/0112150

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Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics
Dinshaw Balsara ;
Date 6 Dec 2001
Journal J. Comput. Phys., 174(2), 614-648, (2001)
Subject astro-ph
AffiliationPhysics Dept., Univ. of Notre Dame
AbstractIn this paper we present a full-fledged scheme for the second order accurate, divergence-free evolution of vector fields on an adaptive mesh refinement (AMR) hierarchy. We focus here on adaptive mesh MHD. The scheme is based on making a significant advance in the divergence-free reconstruction of vector fields. In that sense, it complements the earlier work of Balsara and Spicer (1999) where we discussed the divergence-free time-update of vector fields which satisfy Stoke’s law type evolution equations. Our advance in divergence-free reconstruction of vector fields is such that it reduces to the total variation diminishing (TVD) property for one-dimensional evolution and yet goes beyond it in multiple dimensions. Divergence-free restriction is also discussed. An electric field correction strategy is presented for use on AMR meshes. The electric field correction strategy helps preserve the divergence-free evolution of the magnetic field even when the time steps are sub-cycled on refined meshes. The above-mentioned innovations have been implemented in Balsara’s RIEMANN framework for parallel, self-adaptive computational astrophysics which supports both non-relativistic and relativistic MHD. Several rigorous, three dimensional AMR-MHD test problems with strong discontinuities have been run with the RIEMANN framework showing that the strategy works very well.
Source arXiv, astro-ph/0112150
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