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research-article

An Implicit Scheme for Nonideal Magnetohydrodynamics

Authors:

Ogden S. Jones,

D.Scott EberhardtAuthors Info & Claims

Journal of Computational Physics, Volume 130, Issue 2

Pages 231 - 242

https://doi.org/10.1006/jcph.1996.5580

Published: 15 January 1997 Publication History

Abstract

A new implicit algorithm is developed for solving the time-dependent, nonideal magnetohydrodynamic equations. It can also be used as an efficient relaxation scheme for steady state solutions. The algorithm is a finite-volume scheme that uses an approximate Riemann solver for the hyperbolic fluxes and central differencing applied on nested control volumes for the parabolic fluxes that arise from the non-ideal terms (i.e., resistivity and viscosity). In one dimension the scheme is second-order accurate in space and time. In two or three dimensions, the accuracy is between first and second order. For the class of problems considered, the implicit formulation is stable for any size time step, thus allowing efficient tracking of slower transients. The implicit operator is inverted using a lower upper symmetric Gauss Seidel iteration. Results from several test cases are presented that show good agreement with analytical solutions and illustrate the advantages of the scheme.

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Cited By

Datta IShumlak U(2023)Computationally efficient high-fidelity plasma simulations by coupling multi-species kinetic and multi-fluid models on decomposed domainsJournal of Computational Physics10.1016/j.jcp.2023.112073483:COnline publication date: 1-May-2023
https://dl.acm.org/doi/10.1016/j.jcp.2023.112073
Deluzet FNegulescu COttaviani MPossanner S(2015)Numerical study of the plasma tearing instability on the resistive time scaleJournal of Computational Physics10.1016/j.jcp.2014.10.003280:C(602-625)Online publication date: 1-Jan-2015
https://dl.acm.org/doi/10.1016/j.jcp.2014.10.003
Jardin S(2012)Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmasJournal of Computational Physics10.1016/j.jcp.2010.12.025231:3(822-838)Online publication date: 1-Feb-2012
https://dl.acm.org/doi/10.1016/j.jcp.2010.12.025
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Index Terms

An Implicit Scheme for Nonideal Magnetohydrodynamics
1. Applied computing
  1. Physical sciences and engineering
    1. Physics
2. Mathematics of computing

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Information

Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 130, Issue 2

January 15, 1997

124 pages

ISSN:0021-9991

Editor:
J. U. Brackbill
Los Alamos National Lab, Los Alamos, NM

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Copyright © Academic Press.

Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 15 January 1997

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Cited By

Datta IShumlak U(2023)Computationally efficient high-fidelity plasma simulations by coupling multi-species kinetic and multi-fluid models on decomposed domainsJournal of Computational Physics10.1016/j.jcp.2023.112073483:COnline publication date: 1-May-2023
https://dl.acm.org/doi/10.1016/j.jcp.2023.112073
Deluzet FNegulescu COttaviani MPossanner S(2015)Numerical study of the plasma tearing instability on the resistive time scaleJournal of Computational Physics10.1016/j.jcp.2014.10.003280:C(602-625)Online publication date: 1-Jan-2015
https://dl.acm.org/doi/10.1016/j.jcp.2014.10.003
Jardin S(2012)Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmasJournal of Computational Physics10.1016/j.jcp.2010.12.025231:3(822-838)Online publication date: 1-Feb-2012
https://dl.acm.org/doi/10.1016/j.jcp.2010.12.025
Han JTang H(2007)An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamicsJournal of Computational Physics10.1016/j.jcp.2006.05.031220:2(791-812)Online publication date: 1-Jan-2007
https://dl.acm.org/doi/10.1016/j.jcp.2006.05.031
Hakim ALoverich JShumlak U(2006)A high resolution wave propagation scheme for ideal Two-Fluid plasma equationsJournal of Computational Physics10.1016/j.jcp.2006.03.036219:1(418-442)Online publication date: 20-Nov-2006
https://dl.acm.org/doi/10.1016/j.jcp.2006.03.036
Reynolds DSamtaney RWoodward C(2006)A fully implicit numerical method for single-fluid resistive magnetohydrodynamicsJournal of Computational Physics10.1016/j.jcp.2006.03.022219:1(144-162)Online publication date: 20-Nov-2006
https://dl.acm.org/doi/10.1016/j.jcp.2006.03.022
Shumlak ULoverich J(2003)Approximate Riemann solver for the two-fluid plasma modelJournal of Computational Physics10.1016/S0021-9991(03)00151-7187:2(620-638)Online publication date: 20-May-2003
https://dl.acm.org/doi/10.1016/S0021-9991%2803%2900151-7
Chacón LKnoll DFinn J(2002)An Implicit, Nonlinear Reduced Resistive MHD SolverJournal of Computational Physics10.1006/jcph.2002.7015178:1(15-36)Online publication date: 1-May-2002
https://dl.acm.org/doi/10.1006/jcph.2002.7015
Warburton TKarniadakis G(1999)A Discontinuous Galerkin Method for the Viscous MHD EquationsJournal of Computational Physics10.1006/jcph.1999.6248152:2(608-641)Online publication date: 1-Jul-1999
https://dl.acm.org/doi/10.1006/jcph.1999.6248

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