Affordable robust moment closures for CFD based on the maximum-entropy hierarchy

The use of moment closures for the prediction of continuum and moderately non-equilibrium flows offers modelling and numerical advantages over other methods. The maximumentropy hierarchy of moment closures holds the promise of robustly hyperbolic stable moment equations, however their are two issues that limit their practical implementation. Firstly, for closures that have a treatment for heat transfer, fluxes cannot be written in closed form and a very expensive iterative procedure is required at every flux evaluation. Secondly, for these same closures, there are physically possible moment states for which the entropy-maximization problem has no solution and the entire framework breaks down. This paper demonstrates that affordable closed-form moment closures that are inspired by the maximum-entropy framework can be proposed. It is known that closing fluxes in the maximum-entropy hierarchy approach a singularity as the region of non-solvability is approached. This paper shows that, far from a disadvantage, this singularity allows for smooth and accurate prediction of shock-wave structure, even for high Mach numbers. The presence of unphysical ‘‘sub-shocks’’ within shock-profile predictions of traditional closures has long been regarded as an unfortunate limitation of the entire moment-closure technique. The realization that smooth shock profiles are, in fact, possible for moment methods with a moderate number of moments greatly increases the method’s applicability to high-speed flows. In this paper, a 5-moment system for a simple onedimensional gas and a 14-moment system for realistic gases are developed and examined. Numerical solution for shock-waves at a variety of incoming flow Mach numbers demonstrate both the robustness and the accuracy of the closures. 2013 Elsevier Inc. All rights reserved.