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Title: Divergence-free magnetohydrodynamics on conformally moving, adaptive meshes using a vector potential method

Abstract

We introduce a novel method for evolving the equations of magnetohydrodynamics (both Newtonian and relativistic) that is capable of maintaining a divergence-free magnetic field (∇ ∙ B=0) on adaptively refined, conformally moving meshes. This way relies on evolving the magnetic vector potential and then using it to reconstruct the magnetic fields. The advantage of this approach is that the vector potential is not subject to a constraint equation in the same way the magnetic field is, and so can be refined and moved in a straightforward way. We test this new method against a wide array of problems from simple Alfvén waves on a uniform grid to general relativistic MHD simulations of black hole accretion on a nested, spherical-polar grid. We find that the code produces accurate results and in all cases maintains a divergence-free magnetic field to machine precision.

Authors:
ORCiD logo [1];  [1];  [1];  [2]
  1. College of Charleston, SC (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
OSTI Identifier:
1527051
Alternate Identifier(s):
OSTI ID: 1557059
Report Number(s):
LLNL-JRNL-753360
Journal ID: ISSN 2590-0552; 939845
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Published Article
Journal Name:
Journal of Computational Physics: X
Additional Journal Information:
Journal Volume: 2; Journal Issue: C; Journal ID: ISSN 2590-0552
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; Magnetohydrodynamics; Adaptive mesh refinement; Divergence constraint; Astrophysics; Magnetic fields

Citation Formats

Fragile, P. Chris, Nemergut, Daniel, Shaw, Payden L., and Anninos, Peter. Divergence-free magnetohydrodynamics on conformally moving, adaptive meshes using a vector potential method. United States: N. p., 2019. Web. doi:10.1016/j.jcpx.2019.100020.
Fragile, P. Chris, Nemergut, Daniel, Shaw, Payden L., & Anninos, Peter. Divergence-free magnetohydrodynamics on conformally moving, adaptive meshes using a vector potential method. United States. doi:10.1016/j.jcpx.2019.100020.
Fragile, P. Chris, Nemergut, Daniel, Shaw, Payden L., and Anninos, Peter. Tue . "Divergence-free magnetohydrodynamics on conformally moving, adaptive meshes using a vector potential method". United States. doi:10.1016/j.jcpx.2019.100020.
@article{osti_1527051,
title = {Divergence-free magnetohydrodynamics on conformally moving, adaptive meshes using a vector potential method},
author = {Fragile, P. Chris and Nemergut, Daniel and Shaw, Payden L. and Anninos, Peter},
abstractNote = {We introduce a novel method for evolving the equations of magnetohydrodynamics (both Newtonian and relativistic) that is capable of maintaining a divergence-free magnetic field (∇ ∙ B=0) on adaptively refined, conformally moving meshes. This way relies on evolving the magnetic vector potential and then using it to reconstruct the magnetic fields. The advantage of this approach is that the vector potential is not subject to a constraint equation in the same way the magnetic field is, and so can be refined and moved in a straightforward way. We test this new method against a wide array of problems from simple Alfvén waves on a uniform grid to general relativistic MHD simulations of black hole accretion on a nested, spherical-polar grid. We find that the code produces accurate results and in all cases maintains a divergence-free magnetic field to machine precision.},
doi = {10.1016/j.jcpx.2019.100020},
journal = {Journal of Computational Physics: X},
number = C,
volume = 2,
place = {United States},
year = {2019},
month = {3}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1016/j.jcpx.2019.100020

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