A finite element method for MHD that preserves energy, cross-helicity, magnetic helicity, incompressibility, and div B = 0

Evan S. Gawlik; François Gay-Balmaz

doi:10.1016/j.jcp.2021.110847

A finite element method for MHD that preserves energy, cross-helicity, magnetic helicity, incompressibility, and div B = 0

Evan S. Gawlik
, François Gay-Balmaz

University of Hawaii

Research output: Contribution to journal › Article › peer-review

Abstract

We construct a structure-preserving finite element method and time-stepping scheme for inhomogeneous, incompressible magnetohydrodynamics (MHD). The method preserves energy, cross-helicity (when the fluid density is constant), magnetic helicity, mass, total squared density, pointwise incompressibility, and the constraint divB=0 to machine precision, both at the spatially and temporally discrete levels.

Original language	English
Article number	110847
Journal	Journal of Computational Physics
Volume	450
DOIs	https://doi.org/10.1016/j.jcp.2021.110847
Publication status	Published - 1 Feb 2022

Keywords

Energy-preserving
Exactly divergence-free
Finite element
Helicity
Magnetohydrodynamics
Structure-preserving

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10.1016/j.jcp.2021.110847

Cite this

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title = "A finite element method for MHD that preserves energy, cross-helicity, magnetic helicity, incompressibility, and div B = 0",

abstract = "We construct a structure-preserving finite element method and time-stepping scheme for inhomogeneous, incompressible magnetohydrodynamics (MHD). The method preserves energy, cross-helicity (when the fluid density is constant), magnetic helicity, mass, total squared density, pointwise incompressibility, and the constraint divB=0 to machine precision, both at the spatially and temporally discrete levels.",

keywords = "Energy-preserving, Exactly divergence-free, Finite element, Helicity, Magnetohydrodynamics, Structure-preserving",

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AU - Gay-Balmaz, François

PY - 2022/2/1

Y1 - 2022/2/1

N2 - We construct a structure-preserving finite element method and time-stepping scheme for inhomogeneous, incompressible magnetohydrodynamics (MHD). The method preserves energy, cross-helicity (when the fluid density is constant), magnetic helicity, mass, total squared density, pointwise incompressibility, and the constraint divB=0 to machine precision, both at the spatially and temporally discrete levels.

AB - We construct a structure-preserving finite element method and time-stepping scheme for inhomogeneous, incompressible magnetohydrodynamics (MHD). The method preserves energy, cross-helicity (when the fluid density is constant), magnetic helicity, mass, total squared density, pointwise incompressibility, and the constraint divB=0 to machine precision, both at the spatially and temporally discrete levels.

KW - Energy-preserving

KW - Exactly divergence-free

KW - Finite element

KW - Helicity

KW - Magnetohydrodynamics

KW - Structure-preserving

UR - https://www.scopus.com/pages/publications/85120415286

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DO - 10.1016/j.jcp.2021.110847

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VL - 450

JO - Journal of Computational Physics

JF - Journal of Computational Physics

M1 - 110847

ER -

A finite element method for MHD that preserves energy, cross-helicity, magnetic helicity, incompressibility, and div B = 0

Abstract

Keywords

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A finite element method for MHD that preserves energy, cross-helicity, magnetic helicity, incompressibility, and div B = 0

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this

A finite element method for MHD that preserves energy, cross-helicity, magnetic helicity, incompressibility, and div B = 0