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

Kinetic equations are difficult to solve numerically due to their highdimensionality. A promising approach for reducing computational cost is thedynamical low-rank algorithm, which decouples the dimensions of the phase spaceby proposing an ansatz as the sum of separable (rank-1) functions in positionand velocity respectively. The fluid asymptotic limit of collisional kineticequations, obtained in the small-Knudsen number limit, admits a low-rankrepresentation when written as $f = Mg$, where $M$ is the local Maxwellian, and$g$ is low-rank. We apply this decomposition to theVlasov-Amp\`{e}re-Fokker-Planck equation of plasma dynamics, considering theasymptotic limit of strong collisions and electric field. We implement ourproposed algorithm and demonstrate the expected improvement in computation timeby comparison to an implementation that evolves the full solution tensor $f$.We also demonstrate that our algorithm can capture dynamics in both the kineticregime, and in the fluid regime with relatively lower computational effort,thereby efficiently capturing the asymptotic fluid limit.

Efficient dynamical low-rank approximation for the Vlasov-Amp\`{e}re-Fokker-Planck system