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

TL;DR

This paper presents a comprehensive set of benchmarks for a conservative spectral solver of the nonlinear Boltzmann equation, demonstrating its efficiency and accuracy across various physical applications.

Contribution

It introduces an expanded implementation of the Galerkin-Petrov spectral algorithm with distributed precomputation, enabling rapid solutions for diverse Boltzmann problems.

Findings

Solutions of homogeneous Boltzmann equations achieved in seconds

Spatially-inhomogeneous problems solved in minutes

Benchmarks validated against theoretical predictions and other solvers

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 against both analytic theoretical predictions and comparisons to other Boltzmann solvers are presented in the context of several domains including weakly ionized plasma, gaseous fluids, and atomic-plasma interaction.