A Unified Gas Kinetic Scheme for Multi-scale and Multi-component Plasma Transport

Abstract: A unified gas kinetic scheme (UGKS) for multi-scale and multi-component plasma transport is constructed. The current scheme is a direct modeling method, where the time evolution solutions from the Vlasov-BGK equations of electron and ion and the Maxwell equations are used to construct a scale-dependent plasma simulation model. As a result, with the changing of modeling scales of mesh size and time step and with a variation of Knudsen number and Larmor radius, the discretized governing equations for a wide range of plasma evolution regimes can be obtained. The physics recovered in UGKS ranges from the Vlasov equation in the kinetic scale to different-type magneto-hydrodynamic (MHD) equations in the hydrodynamic scale. The key dynamics in UGKS is the un-splitting treatment of particle collision, acceleration, and transport in the construction of numerical flux across a cell interface. At the same time, the plasma evolution is coupled with the Maxwell equations in an implicit way, which automatically provides a smooth transition between the Ampere's law and the Ohm's law for the calculation of electric field. The time step of UGKS is not limited by the relaxation time, the cyclotron period, and the speed of light in the MHD regime. The UGKS is validated by numerical test cases, such as the Landau damping and two stream instability in the kinetic regime, and the Brio-Wu shock tube problem and the Orszag- Tang MHD turbulence problem in the hydrodynamic regime. The scheme is also used to study the geospace environment modeling (GEM), such as the challenging magnetic reconnection problem in the transition regime. Overall, the UGKS is a physically reliable multi-scale plasma simulation method. It provides a powerful and unified approach for the study of plasma physics.