A Finite Element Method for MHD that Preserves Energy, Cross-Helicity, Magnetic Helicity, Incompressibility, and div B = 0

2021 ◽  
pp. 110847
Author(s):  
Evan S. Gawlik ◽  
François Gay-Balmaz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Magnetic Helicity ◽  
Element Method

scholarly journals A structure-preserving finite element method for compressible ideal and resistive magnetohydrodynamics

2021 ◽  
Vol 87 (5) ◽  
Author(s):  
Evan S. Gawlik ◽  
François Gay-Balmaz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Magnetic Helicity ◽  
Machine Precision ◽  
Ideal Case ◽  
Conservation Of Energy ◽  
Structure Preserving ◽  
Time Stepping ◽  
The Ideal ◽  
Element Method

We construct a structure-preserving finite element method and time-stepping scheme for compressible barotropic magnetohydrodynamics both in the ideal and resistive cases, and in the presence of viscosity. The method is deduced from the geometric variational formulation of the equations. It preserves the balance laws governing the evolution of total energy and magnetic helicity, and preserves mass and the constraint $\text {div}B = 0$ to machine precision, both at the spatially and temporally discrete levels. In particular, conservation of energy and magnetic helicity hold at the discrete levels in the ideal case. It is observed that cross-helicity is well conserved in our simulation in the ideal case.

Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽  
2019 ◽  
Vol 11 (43) ◽  
pp. 20868-20875 ◽  
Author(s):  
Junxiong Guo ◽  
Yu Liu ◽  
Yuan Lin ◽  
Yu Tian ◽  
Jinxing Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interfacial Effect ◽  
Infrared Photodetector ◽  
The Finite Element Method ◽  
Ferroelectric Domains ◽  
Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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