The linearized Boltzmann equation: Sound-wave propagation in a rarefied gas

An analytical version of the discrete-ordinates method (the ADO method) is used to establish concise and particularly accurate solutions to the problem of sound-wave propagation in a rarefied gas. The analysis and the numerical work are based on a rigorous form of the linearized Boltzmann equation (for rigid-sphere interactions), and in contrast to many other works formulated (for an infinite medium) without a boundary condition, the solution reported here satisfies a boundary condition that models a diffusely-reflecting vibrating plate. In addition and in order to investigate the effect of kinetic models, solutions are developed for the BGK model, the S model, the Gross–Jackson model, as well as for the (newly defined) MRS model and the CES model. While the developed numerical results are compared to available experimental data, emphasis in this work is placed on the solutions of the problem of sound-wave propagation as described by the linearized Boltzmann equation and the five considered kinetic models.