Analysis of an asymptotic preserving scheme for stochastic linear kinetic equations in the diffusion limit

TL;DR

This paper introduces an asymptotic preserving numerical scheme for stochastic linear kinetic equations that remains stable across different regimes, validated through mathematical analysis and numerical tests.

Contribution

The paper develops a novel micro-macro decomposition-based scheme that is uniformly stable in kinetic and diffusive regimes, with rigorous analysis and validation.

Findings

Scheme is mathematically proven to be stable across regimes.

Numerical tests confirm the scheme's accuracy and stability.

Applicable to stochastic linear transport equations in various regimes.

Abstract

We present an asymptotic preserving scheme based on a micro-macro decomposition for stochastic linear transport equations in kinetic and diffusive regimes. We perfom a mathematical analysis and prove that the scheme is uniformly stable with respect to the mean free path of the particles in the simple telegraph model and in the general case. We present several numerical tests which validate our scheme.