A mixed implicit–explicit finite difference scheme for heat transport in magnetised plasmas

An explicit/implicit domain decomposition method is applied to the time-dependent heat-conduction problem in a 2-d, strongly anisotropic medium (a magnetised plasma), using a formulation of the spatial derivatives which avoids the pollution of perpendicular by parallel heat fluxes. The time-stepping at the sub-domain boundaries is done using a DuFort–Frankel scheme, which leads to a time step limit given not by instabilities, but by the damping rate of numerical oscillations driven by inconsistencies in the formulation of initial conditions or the temporal variations in the true physical solution. These limitations can be minimized, however, by aligning the subdomain boundaries as much as possible with magnetic flux surfaces. The time step limit depends on the ratio of the implicit grid spacing to the distance between subdomain boundaries (DuFort–Frankel lines in 2-d, surfaces in 3-d).