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Title: Variational Integration for Ideal MHD with Built-in Advection Equations

Abstract

Newcomb's Lagrangian for ideal MHD in Lagrangian labeling is discretized using discrete exterior calculus. Variational integrators for ideal MHD are derived thereafter. Besides being symplectic and momentum preserving, the schemes inherit built-in advection equations from Newcomb's formulation, and therefore avoid solving them and the accompanying error and dissipation. We implement the method in 2D and show that numerical reconnection does not take place when singular current sheets are present. We then apply it to studying the dynamics of the ideal coalescence instability with multiple islands. The relaxed equilibrium state with embedded current sheets is obtained numerically.

Authors:
 [1];  [1];  [1];  [1]
  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
Contributing Org.:
Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543,USA, Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
OSTI Identifier:
1179782
Report Number(s):
PPPL-5053
DOE Contract Number:
DE-AC02-09CH11466
Resource Type:
Technical Report
Resource Relation:
Related Information: Submitted to Physics of Plasmas
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Computational Physics; Computer Simulation; Magnetohydrodynamics (MHD)

Citation Formats

Zhou, Yao, Qin, Hong, Burby, J. W., and Bhattacharjee, A. Variational Integration for Ideal MHD with Built-in Advection Equations. United States: N. p., 2014. Web. doi:10.2172/1179782.
Zhou, Yao, Qin, Hong, Burby, J. W., & Bhattacharjee, A. Variational Integration for Ideal MHD with Built-in Advection Equations. United States. doi:10.2172/1179782.
Zhou, Yao, Qin, Hong, Burby, J. W., and Bhattacharjee, A. Tue . "Variational Integration for Ideal MHD with Built-in Advection Equations". United States. doi:10.2172/1179782. https://www.osti.gov/servlets/purl/1179782.
@article{osti_1179782,
title = {Variational Integration for Ideal MHD with Built-in Advection Equations},
author = {Zhou, Yao and Qin, Hong and Burby, J. W. and Bhattacharjee, A.},
abstractNote = {Newcomb's Lagrangian for ideal MHD in Lagrangian labeling is discretized using discrete exterior calculus. Variational integrators for ideal MHD are derived thereafter. Besides being symplectic and momentum preserving, the schemes inherit built-in advection equations from Newcomb's formulation, and therefore avoid solving them and the accompanying error and dissipation. We implement the method in 2D and show that numerical reconnection does not take place when singular current sheets are present. We then apply it to studying the dynamics of the ideal coalescence instability with multiple islands. The relaxed equilibrium state with embedded current sheets is obtained numerically.},
doi = {10.2172/1179782},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Aug 05 00:00:00 EDT 2014},
month = {Tue Aug 05 00:00:00 EDT 2014}
}

Technical Report:

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  • Newcomb's Lagrangian for ideal magnetohydrodynamics (MHD) in Lagrangian labeling is discretized using discrete exterior calculus. Variational integrators for ideal MHD are derived thereafter. Besides being symplectic and momentum-preserving, the schemes inherit built-in advection equations from Newcomb's formulation, and therefore avoid solving them and the accompanying error and dissipation. We implement the method in 2D and show that numerical reconnection does not take place when singular current sheets are present. We then apply it to studying the dynamics of the ideal coalescence instability with multiple islands. The relaxed equilibrium state with embedded current sheets is obtained numerically.
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