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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We apply the collision-based hybrid introduced in \cite{hauck} to theBoltzmann equation with the BGK operator and a hyperbolic scaling. An implicittreatment of the source term is used to handle stiffness associated with theBGK operator. Although it helps the numerical scheme become stable with a largetime step size, it is still not obvious to achieve the desired order ofaccuracy due to the relationship between the size of the spatial cell and themean free path. Without asymptotic preserving property, a very restricted gridsize is required to resolve the mean free path, which is not practical. Ourapproaches are based on the noncollision-collision decomposition of the BGKequation. We introduce the arbitrary order of nodal discontinuous Galerkin (DG)discretization in space with a semi-implicit time-stepping method; we employthe backward Euler time integration for the uncollided equation and the 2ndorder predictor-corrector scheme for the collided equation, i.e., both sourceterms in uncollided and collided equations are treated implicitly and onlystreaming term in the collided equation is solved explicitly. This improves thecomputational efficiency without the complexity of the numericalimplementation. Numerical results are presented for various Knudsen numbers topresent the effectiveness and accuracy of our hybrid method. Also, we comparethe solutions of the hybrid and non-hybrid schemes.

A Collision-Based Hybrid Method for the BGK Equation