1D thermal creep channel flow in the BGK approximation by adding and doubling

Abstract

In the past, the method of adding and doubling has received considerable attention as an effective approach to solving the linear transport equation. Here, we consider doubling for the problem of thermal creep in Rarefied Gas Dynamics. The method, called the Discrete/Discrete Ordinates (D/DO) method is in contrast to the well-known Analytical/Discrete Ordinates (A/DO) method. The D/DO method solves the fully discretized transport equation to demonstrate that straightforward numerical approximation also yields high quality numerical solutions. The method combines the fundamental forward Euler evaluation of the matrix exponential with Richardson extrapolation to generate a high quality benchmark. We then generalize the method using Padé approximants for the matrix exponential and present a 7-place benchmark.