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Title: Stabilization of numerical interchange in spectral-element magnetohydrodynamics

Abstract

In this study, auxiliary numerical projections of the divergence of flow velocity and vorticity parallel to magnetic field are developed and tested for the purpose of suppressing unphysical interchange instability in magnetohydrodynamic simulations. The numerical instability arises with equal-order C 0 finite- and spectral-element expansions of the flow velocity, magnetic field, and pressure and is sensitive to behavior at the limit of resolution. The auxiliary projections are motivated by physical field-line bending, and coercive responses to the projections are added to the flow-velocity equation. Their incomplete expansions are limited to the highest-order orthogonal polynomial in at least one coordinate of the spectral elements. Cylindrical eigenmode computations show that the projections induce convergence from the stable side with first-order ideal-MHD equations during h-refinement and p-refinement. Hyperbolic and parabolic projections and responses are compared, together with different methods for avoiding magnetic divergence error. Lastly, the projections are also shown to be effective in linear and nonlinear time-dependent computations with the NIMROD code [C. R. Sovinec, et al., J. Comput. Phys. 195 (2004) 355-386], provided that the projections introduce numerical dissipation.

Authors:
 [1]
  1. Univ. of Wisconsin, Madison, WI (United States). Department of Engineering Physics
Publication Date:
Research Org.:
Univ. of Wisconsin, Madison, WI (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
OSTI Identifier:
1436975
Alternate Identifier(s):
OSTI ID: 1324850
Grant/Contract Number:
FC02-08ER54975; AC02-05CH11231
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 319; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 97 MATHEMATICS AND COMPUTING; MHD computation; Spectral elements; Spectral filtering; Interchange instability

Citation Formats

Sovinec, C. R. Stabilization of numerical interchange in spectral-element magnetohydrodynamics. United States: N. p., 2016. Web. doi:10.1016/j.jcp.2016.04.063.
Sovinec, C. R. Stabilization of numerical interchange in spectral-element magnetohydrodynamics. United States. doi:10.1016/j.jcp.2016.04.063.
Sovinec, C. R. Tue . "Stabilization of numerical interchange in spectral-element magnetohydrodynamics". United States. doi:10.1016/j.jcp.2016.04.063. https://www.osti.gov/servlets/purl/1436975.
@article{osti_1436975,
title = {Stabilization of numerical interchange in spectral-element magnetohydrodynamics},
author = {Sovinec, C. R.},
abstractNote = {In this study, auxiliary numerical projections of the divergence of flow velocity and vorticity parallel to magnetic field are developed and tested for the purpose of suppressing unphysical interchange instability in magnetohydrodynamic simulations. The numerical instability arises with equal-order C0 finite- and spectral-element expansions of the flow velocity, magnetic field, and pressure and is sensitive to behavior at the limit of resolution. The auxiliary projections are motivated by physical field-line bending, and coercive responses to the projections are added to the flow-velocity equation. Their incomplete expansions are limited to the highest-order orthogonal polynomial in at least one coordinate of the spectral elements. Cylindrical eigenmode computations show that the projections induce convergence from the stable side with first-order ideal-MHD equations during h-refinement and p-refinement. Hyperbolic and parabolic projections and responses are compared, together with different methods for avoiding magnetic divergence error. Lastly, the projections are also shown to be effective in linear and nonlinear time-dependent computations with the NIMROD code [C. R. Sovinec, et al., J. Comput. Phys. 195 (2004) 355-386], provided that the projections introduce numerical dissipation.},
doi = {10.1016/j.jcp.2016.04.063},
journal = {Journal of Computational Physics},
number = C,
volume = 319,
place = {United States},
year = {Tue May 10 00:00:00 EDT 2016},
month = {Tue May 10 00:00:00 EDT 2016}
}

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