Multiscale modelling and splitting approaches for fluids composed of Coulomb-interacting particles

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.