Abstract
We propose a Lagrangian numerical algorithm for a time-dependent, anisotropic tem- perature 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 lo- cal and nonlocal 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. Al- gorithmically, 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 par- allel transport term when the perpendicular to parallel transport coefficient ratio χ⊥/χ∥ becomes arbitrarily small, and is shown to capture the correct limiting solution when χ⊥/χ∥ → 0. Therefore, the approach is asymptotic-preserving. We demonstrate the ca- pabilities of the scheme with several numerical experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.
