Poiseuille channel flow by adding and doubling

Abstract

The flow of a rarefied gas between two plates of a micro channel, commonly called Poiseuille flow, has been extensively studied in the BGK approximation. In particular, the Analytical Discrete Ordinates (ADO) method determines the velocity profile and flow rate efficiently and accurately. Here, an equally efficient and precise solution is presented using the method of doubling, which however is arguably a numerically simpler and a more natural approach avoiding eigenvalues and eigenvectors. Highly accurate benchmark results for Poiseuille flow are reported for use as a benchmark.