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Title: Constrained-transport magnetohydrodynamics with adaptive mesh refinement in CHARM

Abstract

We present the implementation of a three-dimensional, second-order accurate Godunov-type algorithm for magnetohydrodynamics (MHD) in the adaptive-mesh-refinement (AMR) cosmological code CHARM. The algorithm is based on the full 12-solve spatially unsplit corner-transport-upwind (CTU) scheme. The fluid quantities are cell-centered and are updated using the piecewise-parabolic method (PPM), while the magnetic field variables are face-centered and are evolved through application of the Stokes theorem on cell edges via a constrained-transport (CT) method. The so-called multidimensional MHD source terms required in the predictor step for high-order accuracy are applied in a simplified form which reduces their complexity in three dimensions without loss of accuracy or robustness. The algorithm is implemented on an AMR framework which requires specific synchronization steps across refinement levels. These include face-centered restriction and prolongation operations and a reflux-curl operation, which maintains a solenoidal magnetic field across refinement boundaries. The code is tested against a large suite of test problems, including convergence tests in smooth flows, shock-tube tests, classical two- and three-dimensional MHD tests, a three-dimensional shock-cloud interaction problem, and the formation of a cluster of galaxies in a fully cosmological context. The magnetic field divergence is shown to remain negligible throughout.

Authors:
 [1];  [2]
+ Show Author Affiliations
  1. ETH, Zurich (Switzerland)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21), Scientific Discovery through Advanced Computing (SciDAC) (SC21.1 )
OSTI Identifier:
1511331
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
The Astrophysical Journal. Supplement Series
Additional Journal Information:
Journal Volume: 195; Journal Issue: 1; Journal ID: ISSN 0067-0049
Publisher:
American Astronomical Society
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS

Citation Formats

Miniati, Francesco, and Martin, Daniel F. Constrained-transport magnetohydrodynamics with adaptive mesh refinement in CHARM. United States: N. p., 2011. Web. doi:10.1088/0067-0049/195/1/5.
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Miniati, Francesco, & Martin, Daniel F. Constrained-transport magnetohydrodynamics with adaptive mesh refinement in CHARM. United States. https://doi.org/10.1088/0067-0049/195/1/5
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Miniati, Francesco, and Martin, Daniel F. Thu . "Constrained-transport magnetohydrodynamics with adaptive mesh refinement in CHARM". United States. https://doi.org/10.1088/0067-0049/195/1/5. https://www.osti.gov/servlets/purl/1511331.
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@article{osti_1511331,
title = {Constrained-transport magnetohydrodynamics with adaptive mesh refinement in CHARM},
author = {Miniati, Francesco and Martin, Daniel F.},
abstractNote = {We present the implementation of a three-dimensional, second-order accurate Godunov-type algorithm for magnetohydrodynamics (MHD) in the adaptive-mesh-refinement (AMR) cosmological code CHARM. The algorithm is based on the full 12-solve spatially unsplit corner-transport-upwind (CTU) scheme. The fluid quantities are cell-centered and are updated using the piecewise-parabolic method (PPM), while the magnetic field variables are face-centered and are evolved through application of the Stokes theorem on cell edges via a constrained-transport (CT) method. The so-called multidimensional MHD source terms required in the predictor step for high-order accuracy are applied in a simplified form which reduces their complexity in three dimensions without loss of accuracy or robustness. The algorithm is implemented on an AMR framework which requires specific synchronization steps across refinement levels. These include face-centered restriction and prolongation operations and a reflux-curl operation, which maintains a solenoidal magnetic field across refinement boundaries. The code is tested against a large suite of test problems, including convergence tests in smooth flows, shock-tube tests, classical two- and three-dimensional MHD tests, a three-dimensional shock-cloud interaction problem, and the formation of a cluster of galaxies in a fully cosmological context. The magnetic field divergence is shown to remain negligible throughout.},
doi = {10.1088/0067-0049/195/1/5},
journal = {The Astrophysical Journal. Supplement Series},
number = 1,
volume = 195,
place = {United States},
year = {Thu Jun 23 00:00:00 EDT 2011},
month = {Thu Jun 23 00:00:00 EDT 2011}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1088/0067-0049/195/1/5
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Cited by: 30 works
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Figures / Tables:

Fig. 1 Fig. 1: Control volume and discrete representation of physical quantities.
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    Accurate, Meshless Methods for Magneto-Hydrodynamics
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    Self-similar energetics in large clusters of galaxies
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      Figures / Tables found in this record:

      Fig. 1 (p. 7)figure
      Table 1 (p. 20)table
      Fig. 2 (p. 23)figure
      Fig. 3 (p. 25)figure
      Fig. 4. (p. 26)figure
      Fig. 5 (p. 28)figure
      Fig. 6 (p. 29)figure
      Fig. 7 (p. 32)figure
      Fig. 8 (p. 33)figure
      Table 2 (p. 33)table
      Table 3 (p. 34)table
      Table 4 (p. 35)table
      Fig. 10 (p. 36)figure
      Fig. 9 (p. 36)figure
      Table 5 (p. 37)table
      Fig. 11 (p. 38)figure
      Fig. 12 (p. 38)figure
      Fig. 13 (p. 41)figure
      Fig. 15 (p. 45)figure
      Fig. 16 (p. 49)figure
      Fig. 17 (p. 54)figure
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