Benchmarks of a conservative spectral solver for the nonlinear Boltzmann transport equation.

The Boltzmann equation provides the theoretical foundation for plasma physics and aerodynamics, while also appearing across physics in semi-classical contexts. While Monte Carlo techniques have been a robust and mainstream method, difficulties arise when coupled to deterministic fluid and kinetic plasma simulations. Spectral methods also have a long history of being applied to the Boltzmann equation, and recently a Galerkin-Petrov method has been found which is manifestly conservative for the full bilinear collision operator [Gamba & Rjasanow, JCP 2018]. LightningBoltz is an implementation of this algorithm, extended for inelastic collisions, tabulated cross sections, implicit time advance, and adaptive integration techniques. A key feature is the precomputation and online storage of the discrete collision operators, which allows users to solve the transient 1D+3V Boltzmann equation with remarkable efficiency. Several benchmarks across a range of disciplines are presented. Firstly, the artificial constructed solution with Maxwell molecules is shown (including inelastic processes). Next, the collisional Chapman-Enskog predictions for viscocity and thermal diffusivity are reproduced to high accuracy at small Knudsen number. Cross-code comparisons are shown to accurately reproduce the results of: BOLSIG+ for electrons in weakly ionized plasma, and DEGAS2 for neutrals in a 1D scrape-off-layer-like domain. Limitations of the spectral representation are also discussed, and several methods for generalizing the algorithm for broad energy scales will be discussed.