Modeling plasma systems using a domain-hybridized physical model

Abstract

Plasma models have regions of validity that depend on local parameters.In some problems a computationally expensive, high-fidelity model is required in a small subset of the domain while lower-cost reduced models can adequately describe the plasma behavior everywhere else. The goal of this research is to investigate methods for spatially coupling the various plasma models such that the simplest plasma model that is locally valid can maintain global physical fidelity while improving computational efficiency. This research has two primary components. The first component is investigating numerical methods which can efficiently couple the various plasma models. Mixed implicit-explicit (ImEx) temporal solution schemes are investigated to produce schemes which are numerically stable when the time scales of interest span several orders of magnitude, and the physics of interest is dominated by long time scale physics. The spatial discretization method of choice is based on the discontinuous Galerkin (DG) method. Traditional DG methods are capable of producing numerical schemes with high spatial accuracy, but produce large and stiff implicit systems. To address this deficiency, the traditional DG scheme is augmented with a hybridized discontinuous Galerkin (HDG) scheme which is specifically designed to handle implicit temporal schemes. The second component of this research is investigating methods for making the plasma model dynamically (re-)decomposed based on local plasma conditions to produce an adaptive scheme. These metrics can be derived by examining the mathematical differences between the plasma models. This approach allows the determination of relative scale on which non-charge-neutral effects are significant, as well as which metrics are dependent on local gradients or purely on local conditions. Key metrics comparing the MHD and two-fluid models include examining charge neutrality, two-temperature effects, Hall effects, and finite-electron-mass effects.