English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We present a novel numerical method for solving the anisotropic diffusionequation in magnetic fields confined to a periodic box which is accurate andprovably stable. We derive energy estimates of the solution of the continuousinitial boundary value problem. A discrete formulation is presented usingoperator splitting in time with the summation by parts finite differenceapproximation of spatial derivatives for the perpendicular diffusion operator.Weak penalty procedures are derived for implementing both boundary conditionsand parallel diffusion operator obtained by field line tracing. We prove thatthe fully-discrete approximation is unconditionally stable. Discrete energyestimates are shown to match the continuous energy estimate given the correctchoice of penalty parameters. A nonlinear penalty parameter is shown to providean effective method for tuning the parallel diffusion penalty and significantlyminimises rounding errors. Several numerical experiments, using manufacturedsolutions, the ``NIMROD benchmark'' problem and a single island problem, arepresented to verify numerical accuracy, convergence, and asymptotic preservingproperties of the method. Finally, we present a magnetic field with chaoticregions and islands and show the contours of the anisotropic diffusion equationreproduce key features in the field.

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields