A particle micro-macro decomposition based numerical scheme for collisional kinetic equations in the diffusion scaling
This work addresses the challenge of simulating collisional kinetic equations in the diffusion scaling, providing a more efficient and stable particle method for researchers in kinetic theory and computational physics.
The authors derive particle schemes for linear kinetic equations in the diffusion limit using micro-macro decomposition, reformulating the system into a non-stiff PDE to enable uniform stability. The schemes are asymptotic-preserving, reduce noise compared to traditional particle methods, and have decreasing computational cost as the system approaches the diffusion limit.
In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part has to be performed, and the stiffness of both these two parts prevent from uniform stability. To overcome this difficulty, the micro-macro system is reformulated into a continuous PDE whose coefficients are no longer stiff, and depend on the time step $Δt$ in a consistent way. This non-stiff reformulation of the micro-macro system allows the use of standard particle approximations for the transport part, and extends the work in [5] where a particle approximation has been applied using a micro-macro decomposition on kinetic equations in the fluid scaling. Beyond the so-called asymptotic-preserving property which is satisfied by our schemes, they significantly reduce the inherent noise of traditional particle methods, and they have a computational cost which decreases as the system approaches the diffusion limit.