On the Holway-Weiss Debate: Convergence of the Grad-Moment-Expansion in Kinetic Gas Theory

Abstract

Moment expansions are used as model reduction technique in kinetic gas theory to approximate the Boltzmann equation. Rarefied gas models based on so-called moment equations became increasingly popular recently. However, in a seminal paper by Holway [Phys. Fluids 7/6, (1965)] a fundamental restriction on the existence of the expansion was used to explain sub-shock behavior of shock profile solutions obtained by moment equations. Later, Weiss [Phys. Fluids 8/6, (1996)] argued that this restriction does not exist. We will revisit and discuss their findings and explain that both arguments have a correct and incorrect part. While a general convergence restriction for moment expansions does exist, it cannot be attributed to sub-shock solutions. We will also discuss the implications of the restriction and give some numerical evidence for our considerations.