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 Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

In this work, we propose a positivity-preserving scheme for solvingtwo-dimensional advection-diffusion equations including mixed derivative terms,in order to improve the accuracy of lower-order methods. The solution to theseequations, in the absence of mixed derivatives, has been studied in detail,while positivity-preserving solutions to mixed derivative terms have receivedmuch less attention. A two-dimensional diffusion equation, for which theanalytical solution is known, is solved numerically to show the applicabilityof the scheme. It is further applied to the Fokker-Planck collision operator intwo-dimensional cylindrical coordinates under the assumption of local thermalequilibrium. For a thermal equilibration problem, it is shown that the schemeconserves particle number and energy, while the preservation of positivity isensured and the steady-state solution is the Maxwellian distribution.

Positivity-preserving scheme for two-dimensional advection-diffusion equations including mixed derivatives