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Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field

Authors:

Sergey YakovlevAuthors Info & Claims

Journal of Computational Physics, Volume 230, Issue 12

Pages 4828 - 4847

https://doi.org/10.1016/j.jcp.2011.03.006

Published: 01 June 2011 Publication History

Abstract

In this paper, central discontinuous Galerkin methods are developed for solving ideal magnetohydrodynamic (MHD) equations. The methods are based on the original central discontinuous Galerkin methods designed for hyperbolic conservation laws on overlapping meshes, and use different discretization for magnetic induction equations. The resulting schemes carry many features of standard central discontinuous Galerkin methods such as high order accuracy and being free of exact or approximate Riemann solvers. And more importantly, the numerical magnetic field is exactly divergence-free. Such property, desired in reliable simulations of MHD equations, is achieved by first approximating the normal component of the magnetic field through discretizing induction equations on the mesh skeleton, namely, the element interfaces. And then it is followed by an element-by-element divergence-free reconstruction with the matching accuracy. Numerical examples are presented to demonstrate the high order accuracy and the robustness of the schemes.

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Cited By

Zampa EBusto SDumbser M(2024)A divergence-free hybrid finite volume / finite element scheme for the incompressible MHD equations based on compatible finite element spaces with a posteriori limitingApplied Numerical Mathematics10.1016/j.apnum.2024.01.014198:C(346-374)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1016/j.apnum.2024.01.014
Ding QLong XMao SXi R(2024)Second Order Unconditionally Convergent Fully Discrete Scheme for Incompressible Vector Potential MHD SystemJournal of Scientific Computing10.1007/s10915-024-02553-x100:1Online publication date: 17-May-2024
https://dl.acm.org/doi/10.1007/s10915-024-02553-x
Liu MFeng XWang X(2023)Implementation of the HLL-GRP solver for multidimensional ideal MHD simulations based on finite volume methodJournal of Computational Physics10.1016/j.jcp.2022.111687473:COnline publication date: 15-Jan-2023
https://dl.acm.org/doi/10.1016/j.jcp.2022.111687
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Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field
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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 230, Issue 12

June, 2011

781 pages

ISSN:0021-9991

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Copyright © Elsevier Inc. © 2011.

Publisher

Academic Press Professional, Inc.

United States

Publication History

Published: 01 June 2011

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Cited By

Zampa EBusto SDumbser M(2024)A divergence-free hybrid finite volume / finite element scheme for the incompressible MHD equations based on compatible finite element spaces with a posteriori limitingApplied Numerical Mathematics10.1016/j.apnum.2024.01.014198:C(346-374)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1016/j.apnum.2024.01.014
Ding QLong XMao SXi R(2024)Second Order Unconditionally Convergent Fully Discrete Scheme for Incompressible Vector Potential MHD SystemJournal of Scientific Computing10.1007/s10915-024-02553-x100:1Online publication date: 17-May-2024
https://dl.acm.org/doi/10.1007/s10915-024-02553-x
Liu MFeng XWang X(2023)Implementation of the HLL-GRP solver for multidimensional ideal MHD simulations based on finite volume methodJournal of Computational Physics10.1016/j.jcp.2022.111687473:COnline publication date: 15-Jan-2023
https://dl.acm.org/doi/10.1016/j.jcp.2022.111687
Jin STang MZhang X(2022)A spatial-temporal asymptotic preserving scheme for radiation magnetohydrodynamics in the equilibrium and non-equilibrium diffusion limitJournal of Computational Physics10.1016/j.jcp.2021.110895452:COnline publication date: 1-Mar-2022
https://dl.acm.org/doi/10.1016/j.jcp.2021.110895
Dao TNazarov M(2022)A High-Order Residual-Based Viscosity Finite Element Method for the Ideal MHD EquationsJournal of Scientific Computing10.1007/s10915-022-01918-492:3Online publication date: 1-Sep-2022
https://dl.acm.org/doi/10.1007/s10915-022-01918-4
He YDong XFeng X(2022)Uniform Stability and Convergence with Respect to of the Three Iterative Finite Element Solutions for the 3D Steady MHD EquationsJournal of Scientific Computing10.1007/s10915-021-01671-090:1Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1007/s10915-021-01671-0
Gao HQiu WSun W(2022)New analysis of mixed FEMs for dynamical incompressible magnetohydrodynamicsNumerische Mathematik10.1007/s00211-022-01341-9153:2-3(327-358)Online publication date: 29-Dec-2022
https://dl.acm.org/doi/10.1007/s00211-022-01341-9
Liu MZhang MLi CShen F(2021)A new locally divergence-free WLS-ENO scheme based on the positivity-preserving finite volume method for ideal MHD equationsJournal of Computational Physics10.1016/j.jcp.2021.110694447:COnline publication date: 15-Dec-2021
https://dl.acm.org/doi/10.1016/j.jcp.2021.110694
Wu KShu C(2021)Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equationsNumerische Mathematik10.1007/s00211-021-01209-4148:3(699-741)Online publication date: 1-Jul-2021
https://dl.acm.org/doi/10.1007/s00211-021-01209-4
Chandrashekar PKumar R(2020)Constraint Preserving Discontinuous Galerkin Method for Ideal Compressible MHD on 2-D Cartesian GridsJournal of Scientific Computing10.1007/s10915-020-01289-884:2Online publication date: 6-Aug-2020
https://dl.acm.org/doi/10.1007/s10915-020-01289-8
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