Deterministic Numerical Schemes for the Boltzmann Equation

This article describes methods for the deterministic simulation of the collisional Boltzmann equation. It presumes that the transport and collision parts of the equation are to be simulated separately in the time domain. Time stepping schemes to achieve the splitting as well as numerical methods for each part of the operator are reviewed, with an emphasis on clearly exposing the challenges posed by the equation as well as their resolution by various schemes.