Analysis of an Asymptotic Preserving Scheme for Linear Kinetic Equations in the Diffusion Limit

A New Asymptotic Preserving Scheme Based on Micro-Macro Formulation for Linear Kinetic Equations in the Diffusion Limit

We propose a new numerical scheme for linear transport equations. It is based on a decomposition of the distribution function into equilibrium and non-equilibrium parts. We also use a projection technique that allows to reformulate the kinetic equation into a coupled system of an evolution equation for the macroscopic density and a kinetic equation for the non-equilibrium part. By using a suita...

Asymptotic-preserving Projective Integration Schemes for Kinetic Equations in the Diffusion Limit

We investigate a projective integration scheme for a kinetic equation in the limit of vanishing mean free path, in which the kinetic description approaches a diffusion phenomenon. The scheme first takes a few small steps with a simple, explicit method, such as a spatial centered flux/forward Euler time integration, and subsequently projects the results forward in time over a large time step on ...

On the asymptotic preserving property of the unified gas kinetic scheme for the diffusion limit of linear kinetic models

The unified gas kinetic scheme (UGKS) of K. Xu et al. [37], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of radiative transfer theory. While such problems exhibit purely diffusive behavior in the optically thick (or small Knudsen) regime, we prove that UGKS is still asymptotic preserving (AP) in this regime, but for the free trans...

An asymptotic-preserving scheme for linear kinetic equation with fractional diffusion limit

ar X iv : 1 60 3 . 03 17 1 v 1 [ m at h . A P ] 1 0 M ar 2 01 6 WELL - BALANCED AND ASYMPTOTIC PRESERVING SCHEMES FOR KINETIC MODELS

Abstract. In this paper, we propose a general framework for designing numerical schemes that have both well-balanced (WB) and asymptotic preserving (AP) properties, for various kinds of kinetic models. We are interested in two different parameter regimes, 1) When the ratio between the mean free path and the characteristic macroscopic length ε tends to zero, the density can be described by (adve...