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A unified gas kinetic scheme (UGKS) for multi-scale and multi-componentplasma transport is constructed. The current scheme is a direct modelingmethod, where the time evolution solutions from the Vlasov-BGK equations ofelectron and ion and the Maxwell equations are used to construct ascale-dependent plasma simulation model. As a result, with the changing ofmodeling scales of mesh size and time step and with a variation of Knudsennumber and Larmor radius, the discretized governing equations for a wide rangeof plasma evolution regimes can be obtained. The physics recovered in UGKSranges from the Vlasov equation in the kinetic scale to different-typemagneto-hydrodynamic (MHD) equations in the hydrodynamic scale. The keydynamics in UGKS is the un-splitting treatment of particle collision,acceleration, and transport in the construction of numerical flux across a cellinterface. At the same time, the plasma evolution is coupled with the Maxwellequations in an implicit way, which automatically provides a smooth transitionbetween the Ampere's law and the Ohm's law for the calculation of electricfield. The time step of UGKS is not limited by the relaxation time, thecyclotron period, and the speed of light in the MHD regime. The UGKS isvalidated by numerical test cases, such as the Landau damping and two streaminstability in the kinetic regime, and the Brio-Wu shock tube problem and theOrszag- Tang MHD turbulence problem in the hydrodynamic regime. The scheme isalso used to study the geospace environment modeling (GEM), such as thechallenging magnetic reconnection problem in the transition regime. Overall,the UGKS is a physically reliable multi-scale plasma simulation method. Itprovides a powerful and unified approach for the study of plasma physics.

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