Physically-Realizable Hyperbolic Moment Closures for Predicting Non-Equilibrium Gaseous Flows

Moment closures of gaskinetic theory offer a method for the prediction of non-equilibrium flows which have a wider range of validity than standard continuum methods, such as solution of the Navier-Stokes equations, and can be much more computationally efficient than particle-based techniques, such as Direct Simulation Monte Carlo (DSMC). Moment methods yield systems of first-order partial differential equations in weak-conservation form. Such systems can have computational advantages as they require only the numerical evaluation of first derivatives. One hierarchy of moment closures which seem to have many desirable mathematical properties are those which assume the distribution function is always that which maximizes entropy for a given finite set of velocity moments. These maximum-entropy systems, however, suffer from a major drawback: there exist physically realizable moment values for which a maximumentropy distribution function does not exist. In these regions the moment equations break down and become ill-posed. This paper demonstrates a correction which can be used to remedy this deficiency in maximumentropy closures. Several features of the resulting physically-realizable moment closures are described and computational solutions of the proposed moment system are presented for several flow problems for a one-dimensional gas.