A fast solver for the spatially homogeneous electron Boltzmann equation
<|reference_start|>A fast solver for the spatially homogeneous electron Boltzmann equation: We present a numerical method for the velocity-space, spatially homogeneous, collisional Boltzmann equation for electron transport in low-temperature plasma (LTP) conditions. Modeling LTP plasmas is useful in many applications, including advanced manufacturing, material processing, semiconductor processing, and hypersonics, to name a few. Most state-of-the-art methods for electron kinetics are based on Monte-Carlo sampling for collisions combined with Lagrangian particle-in-cell methods. We discuss an Eulerian solver that approximates the electron velocity distribution function using spherical harmonics (angular components) and B-splines (energy component). Our solver supports electron-heavy elastic and inelastic binary collisions, electron-electron Coulomb interactions, steady-state and transient dynamics, and an arbitrary nmber of angular terms in the electron distribution function. We report convergence results and compare our solver to two other codes: an in-house particle Monte-Carlo ethod; and Bolsig+, a state-of-the-art Eulerian solver for electron transport in LTPs. Furthermore, we use our solver to study the relaxation time scales of the higher-order anisotropic correction terms. Our code is open-source and provides an interface that allows coupling to multiphysics simulations of low-temperature plasmas.<|reference_end|>
@article{fernando2024a,
    title={A fast solver for the spatially homogeneous electron Boltzmann equation},
    author={Milinda Fernando and Daniil Bochkov and James Almgren-Bell and Todd
  Oliver and Robert Moser and Philip Varghese and Laxminarayan Raja and George
  Biros},
    journal={arXiv preprint arXiv:2409.00207},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.00207},
    primaryClass={physics.plasm-ph cs.CE cs.NA math.NA physics.comp-ph}
}