基于粒子微宏观分解的数值方案用于扩散尺度下的碰撞动能方程
A particle micro-macro decomposition based numerical scheme for collisional kinetic equations in the diffusion scaling
AI总结：
本文提出基于微宏观分解的粒子方案，用于线性动能方程的扩散极限情况，通过重构微宏观系统为连续PDE，减少刚性，提升稳定性与计算效率。
摘要：
本文推导了基于微宏观分解的粒子方案，用于线性动能方程在扩散极限下的求解。由于微部分的粒子近似，需分离传输与碰撞部分，二者刚性阻止统一稳定性。为克服此困难，将微宏观系统重构为连续PDE，其系数不再刚性，且一致依赖时间步Δt。此非刚性重构允许使用标准粒子近似处理传输部分，并扩展了[5]中在流体尺度下应用微宏观分解于动能方程的工作。除了满足所谓的渐近保持性质外，这些方案显著降低了传统粒子方法的固有噪声，并且随着系统接近扩散极限，计算成本降低。
英文摘要：
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.
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