A Blended Finite Element Method for Multi-fluid Plasma Modeling

Abstract

In a multi-fluid plasma model electrons and ions are represented as separate fluids that interact through collisions and electromagnetic fields. The model encapsulates physics that spans a vast range of temporal and spatial scales, which renders the model stiff and consequently difficult to solve numerically. To address the large range of time scales, a blended continuous and discontinuous Galerkin method is proposed, where ions are modeled using an explicit Runge-Kutta discontinuous Galerkin method while the electrons and electromagnetic fields are modeled using an implicit continuous Galerkin method. This approach is able to capture large-gradient ion physics like shock formation, while resolving high-frequency electron dynamics in a computationally efficient manner. The convergence properties of the method are analyzed and the method is tested on an electromagnetic shock problem. The numerical method produces results comparable with current state-of-the-art finite volume and discontinuous Galerkin methods, while decreasing the computational time for cases where realistic ion-to-electron mass ratios are used, and realistic speed-of-light to thermal speed ratios are needed. The method is used to study Inertial Confinement Fusion (ICF) fuel species separation where multi-fluid effects are relevant, and the high pressure gradient experienced by the ions causes them to shock, separate, and generate large electric fields. In addition, it is shown that single-fluid plasma codes can overestimate the neutron yield in ICF. For validation purposes, simulation results are compared with experimental data. A meaningful comparison requires the quantification of uncertainties in simulations. The uncertainties in the method are quantified using the multi-level Monte Carlo (MMC) method. The method reduces the computational cost over the standard Monte Carlo method by using multiple levels of discretization to calculate the statistical information of a given model. The MMC method is applied to the Geospace Environment Modeling (GEM) magnetic reconnection challenge problem, in which a reconnected flux is calculated for a given set of initial conditions. A reconnection flux variation envelope is provided, which provides a more rigorous approach to comparing simulation results to from different plasma models. In addition, unbounded domains necessary to allow material and fields to leave the computational domain are modeled using a combined lacuna-based open boundary conditions (LOBC) and perfectly matched layers (PML). This combined method is applied to the electromagnetic wave-pulse, and is shown to considerably reduce reflections from the boundaries. Combining this work addresses some the challenges of high-fidelity modeling of plasmas, and demonstrates the utility of novel numerical techniques that allow for simulation of experimentally-relevant physics over a large range of scales.