Multidisciplinary benchmarks of a conservative spectral solver for the nonlinear Boltzmann equation

Abstract

The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and plasma physics. While these approximations are appropriate in their respective domains, they can be violated in niche but diverse applications which require direct numerical solution of the original nonlinear Boltzmann equation. An expanded implementation of the Galerkin–Petrov conservative spectral algorithm is employed to study a wide variety of physical problems. Enabled by distributed precomputation, solutions of the spatially homogeneous Boltzmann equation can be achieved in seconds on modern personal hardware, while spatially-inhomogeneous problems are solvable in minutes. Several benchmarks are presented focusing on accuracy compared to both analytic theoretical predictions and other Boltzmann solvers. These benchmarks span several physical domains including weakly ionized plasma, gaseous fluids, and atomic-plasma interaction.