Generalized UGK scheme in the diffusive

TL;DR

This paper extends the unified gas kinetic scheme (UGKS) to linear kinetic models with non-isotropic scattering and Fokker-Planck models, demonstrating its asymptotic preserving property in diffusive and free transport regimes through numerical validation.

Contribution

The work introduces a generalized UGKS applicable to complex kinetic models with anisotropic scattering, maintaining asymptotic preserving properties across regimes.

Findings

Effective in diffusive regimes with non-isotropic scattering

Maintains asymptotic preserving property in free transport limit

Numerical experiments confirm robustness and accuracy

Abstract

The unified gas kinetic scheme (UGKS) was initially designed to address multiscale challenges in rarefied gas dynamics and then extended to radiative transfert theory, as described by BGK like relaxation models. In this work, we extend its application to linear kinetic models with non isotropic scattering collision operators, as well as Fokker-Planck models . These problems typically exhibit a fully diffusive nature in the optically thick limit (corresponding to a small Knudsen number). It still leads to an asymptotic preserving (AP) property not only in this diffusive regime but also in the free transport limit. A series of numerical experiments confirm the effectiveness of the approach.