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Title: An asymptotic-preserving Lagrangian algorithm for the time-dependent anisotropic heat transport equation

We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The numerical implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a Lagrangian (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while the second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the numerical pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X /X becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L2/X1L2 → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport acrossmore » a magnetic island.« less
 [1] ;  [2] ;  [3]
  1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
  2. Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
  3. Univ. of Tennessee, Knoxville, TN (United States)
Publication Date:
OSTI Identifier:
DOE Contract Number:
DE-AC05-00OR22725; DE-AC52-06NA25396
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 272
Research Org:
Oak Ridge National Laboratory (ORNL)
Sponsoring Org:
SC USDOE - Office of Science (SC)
Contributing Orgs:
Los Alamos National Laboratory, NM (United States)
Country of Publication:
United States
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY asymptoticpreservingmethods; anisotropictransport; paralleltransport; operator-splitting