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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we present a conservative semi-Lagrangian finite-differencescheme for the BGK model. Classical semi-Lagrangian finite difference schemes,coupled with an L-stable treatment of the collision term, allow large timesteps, for all the range of Knudsen number. Unfortunately, however, suchschemes are not conservative. There are two main sources of lack ofconservation. First, when using classical continuous Maxwellian, conservationerror is negligible only if velocity space is resolved with sufficiently largenumber of grid points. However, for a small number of grids in velocity spacesuch error is not negligible, because the parameters of the Maxwellian do notcoincide with the discrete moments. Secondly, the non-linear reconstructionused to prevent oscillations destroys the translation invariance which is atthe basis of the conservation properties of the scheme. As a consequence theschemes show a wrong shock speed in the limit of small Knudsen number. To treatthe first problem and ensure machine precision conservation of mass, momentumand energy with a relatively small number of velocity grid points, we replacethe continuous Maxwellian with the discrete Maxwellian introduced by Mieussens.The second problem is treated by implementing a conservative correctionprocedure based on the flux difference form. In this way we can construct aconservative semi-Lagrangian scheme which is Asymptotic Preserving (AP) for theunderlying Euler limit, as the Knudsen number vanishes. The effectiveness ofthe proposed scheme is demonstrated by extensive numerical tests.

High order conservative Semi-Lagrangian scheme for the BGK model of the Boltzmann equation