A Unified Gas Kinetic Scheme for Continuum and Rarefied Flows V: Multiscale and Multi-Component Plasma Transport (Communications in Computational Physics, 2017)
As a continuation of developing multiscale method for the transport phenomena,a unified gas kinetic scheme (UGKS) for multi-scale and multi-componentplasma simulation is constructed. The current scheme is a direct modeling method,where the time evolution solutions from the Vlasov-BGK equations of electron and ionand the Maxwell equations are used to construct a scale-dependent plasma simulationmodel. The modeling scale used in the UGKS is the mesh size scale, which canbe comparable to or much larger than the local mean free path. As a result, with thevariation of modeling scales in space and time through the so-called cell's Knudsennumber and normalized Larmor radius, the discretized governing equations can recovera wide range of plasma evolution from the Vlasov equation in the kinetic scale todifferent-type of magnetohydrodynamic (MHD) equations in the hydrodynamic scale.The UGKS provides a general evolution model, which goes to the Vlasov equationin the kinetic scale and many types of MHD equations in the hydrodynamic scale,such as the two fluids model, the Hall, the resistive, and the ideal MHD equations.All current existing governing equations become the subsets of the UGKS, and theUGKS bridges these distinguishable governing equations seamlessly. The constructionof UGKS is based on the implementation of physical conservation laws and theun-splitting treatment of particle collision, acceleration, and transport in the constructionof a scale-dependent numerical flux across a cell interface. At the same time,the discretized plasma evolution equations are coupled with the Maxwell equationsfor electro-magnetic fields, which also cover a scale-dependent transition between theAmpère's law and the Ohm's law for the calculation of electric field. The time stepof UGKS is not limited by the relaxation time, the cyclotron period, and the speed oflight in the ideal-MHD regime. Our scheme is able to give a physically accurate solutionfor plasma simulation with a wide range of Knudsen number and normalizedLarmor radius. It can be used to study the phenomena from the Vlasov limit to the scale of plasma skin depth for the capturing of two-fluid effect, and the phenomenain the plasma transition regime with a modest Knudsen number and Larmor radius.The UGKS is validated by numerical test cases, such as the Landau damping and twostream instability 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 the challengingmagnetic reconnection problem in the transition regime. At the same time, the magneticreconnection mechanism of the Sweet-Parker model and the Hall effect model canbe connected smoothly through the variation of Larmor radius in the UGKS simulations.Overall, the UGKS is a physically reliable multi-scale plasma simulation method,and it provides a powerful and unified approach for the study of plasma physics.