Analysis of an asymptotic preserving scheme for stochastic linear kinetic equations in the diffusion limit
This work provides a rigorous mathematical foundation for numerical methods in stochastic kinetic equations, relevant for researchers in computational physics and applied mathematics.
The authors develop and analyze an asymptotic preserving scheme for stochastic linear kinetic equations, proving uniform stability across kinetic and diffusive regimes, and validate it with numerical tests.
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.