论文标题
在扩散缩放中的Vlasov-BGK方程的混合动力学/流体数值方法
Hybrid Kinetic/Fluid numerical method for the Vlasov-BGK equation in the diffusive scaling
论文作者
论文摘要
本文提出了一种用于扩散缩放的线性碰撞动力学方程的混合数值方法。该方法的目的是通过利用渐近流体模型的较低维度来降低动力学方程的计算成本，同时减少后一种方法引起的误差。它依赖于通过带动方法来获得动态域分解的两个标准。第一个标准量化了距离局部均衡的速度多远。粒子的分布函数是。第二个仅取决于整个计算域上可用的宏观数量。界面条件是使用微麦克罗分解的，该方法比标准的全动力学方法要高得多。还研究了混合方法的某些特性，例如质量保存。
This paper presents a hybrid numerical method for linear collisional kinetic equations with diffusive scaling. The aim of the method is to reduce the computational cost of kinetic equations by taking advantage of the lower dimensionality of the asymptotic fluid model while reducing the error induced by the latter approach. It relies on two criteria motivated by a pertubative approach to obtain a dynamic domain decomposition. The first criterion quantifies how far from a local equilibrium in velocity the distribution function of particles is. The second one depends only on the macroscopic quantities that are available on the whole computing domain. Interface conditions are dealt with using a micro-macro decomposition and the method is significantly more efficient than a standard full kinetic approach. Some properties of the hybrid method are also investigated, such as the conservation of mass.
