ABSTRACT We consider fluids composed of Coulomb-interacting particles, which aremodelled by the Fokker--Planck equation with a collision operator.Based on modelling the transport and collision of the particles,we propose new, computationally efficient, algorithms based on splitting the equations of motion into a global Newtonian transport equation, where the effects of an external electric field are considered, and a local Coulomb interaction stochastic differential equation, which determinesthe new velocities of the particle. Two different numerical schemes, one deterministic and the other stochastic, as well as an Hamiltonian splitting approach, are proposed for coupling the interactionand transport equations. Results are presented for two- and multi-particle systems with different approximations for the Coulomb interaction.Methodologically, the transport part is modelled by thekinetic equations and the collision part is modelled bythe Langevin equations with Coulomb collisions.Such splitting approaches allow concentrating on different solver methodsfor each different part. Further, we solve multiscale problems involving an external electrostatic field.We apply a multiscale approach so that we can decompose the different time-scales of the transport and the collision parts.We discuss the benefits of the different splitting approaches and theirnumerical analysis.

中文翻译：

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由库仑相互作用粒子组成的流体的多尺度建模和分裂方法

摘要 我们考虑由库仑相互作用粒子组成的流体，这些粒子由带有碰撞算子的 Fokker--Planck 方程建模。基于对粒子的传输和碰撞建模，我们提出了基于分解方程的新的计算效率高的算法运动进入全局牛顿输运方程，其中考虑了外部电场的影响，以及局部库仑相互作用随机微分方程，它确定了粒子的新速度。提出了两种不同的数值方案，一种是确定性的，另一种是随机的，以及哈密顿分裂方法，用于耦合相互作用和输运方程。结果显示为具有不同库仑相互作用近似值的两粒子和多粒子系统。输运部分由动力学方程建模，碰撞部分由具有库仑碰撞的朗之万方程建模。这种拆分方法允许针对每个不同部分专注于不同的求解方法。此外，我们解决了涉及外部静电场的多尺度问题。我们应用了多尺度方法，以便我们可以分解运输和碰撞部分的不同时间尺度。我们讨论了不同分裂方法的好处及其数值分析。