High-order moment closures for fluid models in weakly-ionized plasmas

A high-fidelity characterization of the transport of mass, momentum, and energy between different particle species is fundamental in understanding reacting, partially-ionized non-equilibrium plasmas. Under these conditions, the distribution functions of the charged species are usually far from being Maxwellian, which has an important impact on the plasma properties. For this reason, classic fluid models (based on the resolution of the mass, momentum and energy conservation equations) usually fail to fully describe, in a self-consistent manner, these kinetic effects. In this work, we propose models based on the resolution of higher-order moment equations. These methods involve two main difficulties: the closure of the fluxes and the characterization of the multi-component collisional effects. Regarding the flux closure models, in this talk we will review different mathematical methods such as the Grad's method, the quadrature method of moments and entropy-based closures. We will show the advantages and disadvantages of each of them for describing ions and electrons in gas discharges under different pressures. Regarding the collisional terms, we will show how to self-consistently include the collisional exchanges of higher-order moments, including elastic, inelastic, and reactive collisions. The numerical implementation of these methods will be discussed and the numerical solutions will be benchmarked to kinetic solutions such as particle-in-cell simulations as well as two-term Boltzmann and direct Monte-Carlo simulations.