A fast spectral solver for the nonlinear Boltzmann equation

Recent advances in applied mathematics have brought direct solution of the Boltzmann equation within reach of practical applications. The Galerkin-Petrov approach developed by Gamba and Rjasanow [1] is shown to be particularly efficient. LightningBoltz is a newly developed implementation of this algorithm, generalized for non-standard Gaussian quadrature rules and inelastic collisions. Collision matrices are pre-computed and stored in an online database. Such a tool will be useful for studying many kinetic problems in neutral gases and weakly-ionized plasmas, particularly when atomic and/or molecular excitation is important. Such applications include discharges, lightning, reentry communications blackout, divertor detachment, and more.

[1] Gamba and Rjasanow. "Galerkin-Petrov approach for the Boltzmann equation".
Journal of Computational Physics 366:341 (2018)