1. A fast solver for the spatially homogeneous electron Boltzmann equation
- Author
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Fernando, Milinda, Bochkov, Daniil, Almgren-Bell, James, Oliver, Todd, Moser, Robert, Varghese, Philip, Raja, Laxminarayan, and Biros, George
- Subjects
Physics - Plasma Physics ,Computer Science - Computational Engineering, Finance, and Science ,Mathematics - Numerical Analysis ,Physics - Computational Physics - Abstract
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.
- Published
- 2024