Development of globally hyperbolic one-dimensional moment closures based on orthogonal polynomials

The use of moment closure techniques for the prediction of non-equilibrium flows has gained in popularity in the past decades. However, many moment models lack robustness which make them impractical for many engineering applications. Ideally, moment models should always predict realizable moments while maintaining global hyperbolicity and yielding a system in balance-law form. Quadrature-based methods have been shown to offer promising alternatives to more traditional moment methods. Building on the works by Fox and Laurent, a novel approach to moment closure construction is presented. This technique is used to build a new robustly hyperbolic hierarchy for closures with even numbers of moments. Numerical solutions for a typical Riemann problem along with shock waves at a variety of incoming flow Mach numbers are used to compare the robustness and accuracy of the various models.