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Title: Higher Order Lagrange Finite Elements In M3D

Abstract

The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemes have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles.

Authors:
; ; ; ; ; ;
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC) (US)
OSTI Identifier:
836490
Report Number(s):
PPPL-4032
TRN: US0500614
DOE Contract Number:  
AC02-76CH03073
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: 17 Dec 2004
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALIGNMENT; ANISOTROPY; CARTESIAN COORDINATES; TRANSPORT; COMPUTATIONAL PHYSICS; COMPUTER SIMULATION; FINITE ELEMENT METHOD

Citation Formats

Chen, J, Strauss, H R, Jardin, S C, Park, W, Sugiyama, L E, Fu, G, and Breslau, J. Higher Order Lagrange Finite Elements In M3D. United States: N. p., 2004. Web. doi:10.2172/836490.
Chen, J, Strauss, H R, Jardin, S C, Park, W, Sugiyama, L E, Fu, G, & Breslau, J. Higher Order Lagrange Finite Elements In M3D. United States. https://doi.org/10.2172/836490
Chen, J, Strauss, H R, Jardin, S C, Park, W, Sugiyama, L E, Fu, G, and Breslau, J. Fri . "Higher Order Lagrange Finite Elements In M3D". United States. https://doi.org/10.2172/836490. https://www.osti.gov/servlets/purl/836490.
@article{osti_836490,
title = {Higher Order Lagrange Finite Elements In M3D},
author = {Chen, J and Strauss, H R and Jardin, S C and Park, W and Sugiyama, L E and Fu, G and Breslau, J},
abstractNote = {The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemes have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles.},
doi = {10.2172/836490},
url = {https://www.osti.gov/biblio/836490}, journal = {},
number = ,
volume = ,
place = {United States},
year = {2004},
month = {12}
}