A 14-moment maximum-entropy system of equations is applied to the description of non-equilibrium electrons in crossed electric and magnetic fields and in the presence of low collisionality, a characteristic of low-temperature plasma devices. The flexibility of this formulation is analyzed through comparison with analytical results for steady-state non-equilibrium velocity distribution functions and against particle-based solutions of the time-dependent kinetic equation. Electric and magnetic source terms are derived for the 14-moment equations, starting from kinetic theory. A simplified collision term based on the Bhatnagar–Gross–Krook operator is formulated to describe the collision of electrons with background neutrals, accounting for the large mass disparity and energy exchange. An approximated expression is proposed for the collision frequency, to include the effect of the electrons' drift velocity, showing good accuracy in the considered conditions. The capabilities of the proposed 14-moment closure to accurately capture the non-equilibrium behavior of electrons for space homogeneous problems under conditions representative of those found in Hall thrusters are demonstrated.

The use of moment-closure methods to predict continuum and moderately rarefied flow offers many modelling and numerical advantages over traditional methods. The maximumentropy family of moment closures offers models described by hyperbolic systems of balance laws. In particular, the twenty-one moment model of the maximum-entropy hierarchy offers a hyperbolic treatment of viscous flows exhibiting heat transfer. This twenty-one moment model has the ability to provide accurate solutions where the Navier-Stokes equations lose physical validity due to the solution being too far from local equilibrium. Furthermore, its first-order hyperbolic nature offers the potential for improved numerical accuracy as well as a decreased sensitivity to mesh quality. Unfortunately, higher-order maximum-entropy closures cannot be expressed in closed form. The only known affordable option is to propose approximations. Previous approximations to the fourteen-moment maximum-entropy model have been proposed [M c Donald and Torrilhon, 2014]. Although this fourteen-moment model also predicts viscous flow with heat transfer, the necessary moments to close the system renders it more difficult to approximate accurately than the twenty-one moment model. The proposed approximation for the fourteen-moment model also has realizable states for which hyperbolicity is lost.Unfortunately, the velocity distribution function associated with the twenty-one moment model is an exponential of a fourth-order polynomial. Such a function cannot be integrated in closed form, resulting in closing fluxes that can only be obtained through complex numerical methods. The goal of this work is to present a new approximation to the closing fluxes that respect the maximum-entropy philosophy as closely as possible. Preliminary results show that a proposed approximation is able to provide shock predictions that are in good agreement with the Boltzmann equation and surpassing the prediction of the Navier-Stokes equations. Furthermore, Couette flow results as well as lid-driven cavity flows are computed using a novel approach to Knudsen layer boundary conditions. A dispersion analysis as ii well as an investigation of the hyperbolicity of the model is also shown. The Couette flow results are compared against Navier-Stokes and the free-molecular analytical solutions for a varying Knudsen number, for which the twenty-one moment model show good agreement over the domain. The shock-tube problem is also computed for different Knudsen numbers. The results are compared with the one obtained by directly solving the BGK equation. Finally, the lid-driven cavity flow computed with the twenty-one moment model shows good agreement with the direct simulation Monte-Carlo (DSMC) solution.