The Department of Applied Mathematics weekly seminar is given by scholars and researchers working in applied mathematics, broadly interpreted.
Title: Capturing Multiscale Physics using High Fidelity Continuum Plasma Models
Abstract: Plasmas are composed of a large number of charged and neutral particles that interact through electromagnetic forces and collisions over a wide range of temporal and spatial scales to produce collective dynamics. The discrete nature of the plasma particles, their large number, and the wide range of interaction scales make a many-body treatment computationally prohibitive. A statistical treatment evolves the probability density function for each particle species in phase space (x,v) and produces the more manageable but six-dimensional kinetic model, which is typically considered to provide the highest physical fidelity. Assumptions related to thermodynamic relaxation reduce the kinetic model through velocity moments to retain more limited information about the distribution function at each position (x). The moment models, e.g. 5N, 10N, and 13N, are three dimensional and thereby offer substantial computational acceleration compared to the kinetic model. The validity of the assumptions and the resulting moment models depends on local plasma parameters such as collisionality, charge neutrality, and magnetization. Such considerations are necessary when selecting the appropriate model for simulations. Expressing the continuum plasma models in a consistent formulation avails the use of high-order representations, such as finite element methods, and simplifies hybridization. Solutions using the discontinuous Galerkin method will be described, where the governing equations are expressed in a balance law form, an approximate Riemann solver is developed for evaluating inter-element numerical fluxes, and Runge-Kutta methods perform the temporal advance. The computational methods are applied to the GEM collisionless magnetic reconnection problem and the magnetized Kelvin-Helmholtz instability. Spatially localized deviations away from thermodynamic equilibrium are investigated, as well as the resulting agreement and disagreement of global solution metrics between plasma models of differing fidelity. The results suggest opportunities to hybridize by applying the simplest, locally valid plasma model and developing strategies to couple the models across subdomain boundaries.