Stabilization of numerical interchange in spectralelement 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 equalorder C^{0} finite and spectralelement 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 fieldline bending, and coercive responses to the projections are added to the flowvelocity equation. Their incomplete expansions are limited to the highestorder 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 firstorder idealMHD equations during hrefinement and prefinement. 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 timedependent computations with the NIMROD code [C. R. Sovinec, et al., J. Comput. Phys. 195 (2004) 355386], provided that the projections introduce numerical dissipation.
 Authors:

 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) (SC24)
 OSTI Identifier:
 1436975
 Alternate Identifier(s):
 OSTI ID: 1324850
 Grant/Contract Number:
 FC0208ER54975; AC0205CH11231
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 319; Journal Issue: C; Journal ID: ISSN 00219991
 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 spectralelement magnetohydrodynamics. United States: N. p., 2016.
Web. doi:10.1016/j.jcp.2016.04.063.
Sovinec, C. R. Stabilization of numerical interchange in spectralelement magnetohydrodynamics. United States. doi:10.1016/j.jcp.2016.04.063.
Sovinec, C. R. Tue .
"Stabilization of numerical interchange in spectralelement 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 spectralelement 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 equalorder C0 finite and spectralelement 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 fieldline bending, and coercive responses to the projections are added to the flowvelocity equation. Their incomplete expansions are limited to the highestorder 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 firstorder idealMHD equations during hrefinement and prefinement. 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 timedependent computations with the NIMROD code [C. R. Sovinec, et al., J. Comput. Phys. 195 (2004) 355386], 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 = {2016},
month = {5}
}
Web of Science