The study and characterization of plasma flows is of significant interest in many disciplines of engineering and science. Of particular interest is the study and development of plasma-based electric propulsion devices. Plasma flows can exhibit complex behavior depending upon parameter regime and the interaction with applied and induced electromagnetic fields. Further, due to their typically extreme environments, space plasma flows are difficult to investigate with terrestrial experiments. The complexity of plasma flow governing equations typically renders analytical solutions impossible for all but the simplest problems. Thus, the development of more capable physical models and numerical tools for computer simulation is an important research focus. Over the last two decades, the Gas-Kinetic Scheme (GKS) has been demonstrated to be a highly capable solver for a wide range of gas-dynamics flows, from incompressible to rarefied and hypersonic. Further, it has also been shown to work well for ideal, resistive, and Hall magnetohydrodynamics. This dissertation aims to develop the theoretical framework for a gas-kinetic scheme for a singly-charged ion-electron two-fluid plasma. The approach is to apply a Method-of-Characteristics (MoC) - based solution to the Boltzmann equation for each species with the Bhatnagar-Gross-Krook (BGK) collision operator modeling the species self-collisions. In the Boltzmann-BGK (B-BGK) equation the inter-species collisions are modeled as a resistive force on each species. The derived approximate MoC solution renders the resulting particle characteristic trajectories linear in physical space. To model the non-equilibrium effects of collisions, a Chapman-Enskog (CE) type expansion for each species is performed, which captures Finite-Larmor-Radius (FLR) effects on the stress tensor and the heat flux. To consistently couple the ion and electron fluids to the electromagnetic fields, the Perfectly Hyperbolic Maxwell's (PHM) equations are used, which incorporate the constraints of Gauss' Law for the Electric and Magnetic Fields into their temporal evolution. The Two-Fluid Plasma GKS (TFPGKS) scheme is implemented by using Weighted Essentially-Non-Oscillatory (WENO) interpolation for cell interface reconstruction of the flow variables, while a Lax-Friedrichs - type approach is used for the PHM equations. A semi-analytic analysis of the derived fluxes compared to existing models demonstrates the magnetized asymptotic behavior which produces the expected anisotropy in the transport properties. The scheme is benchmarked against analytic solutions for the linearized governing equations. It is further validated against published results for several canonical problems, including the Electromagnetic Shock and Ion Acoustic Solitons. Finally, a parametric study of collisional electromagnetic shocks demonstrates the capabilities of the new TFPGKS scheme over more naive previous implementations. Overall, the work demonstrates the promise of the GKS approach to simulating plasma flows over a wide parameter range.
ETD Chair
Girimaji, Sharath Professor and Head, Holder of Wofford Cain Chair II
