A unified method for the prediction of continuum and transition-regime gas flows - James McDonald

Abstract

The accurate prediction of transition-regime flows has traditionally been difficult.  Continuum models are inaccurate in this regime and particle-based methods become very expensive.  Hyperbolic moment methods have held the promise of offering new models that remain accurate in the transition regime while maintaining computational costs similar to continuum treatments.  Such methods could therefore be used to simulate both continuum- and transition-regime flows, and, if necessary, could be coupled to particle-based methods at much higher Knudsen numbers than continuum treatments.  Unfortunately, classical moment methods suffer from a range of issues, including: a restricted region of well-posedness, exorbitant computational cost associated with closures that cannot be written in closed form, and spurious artificial discontinuities caused by the wavelike behaviourof hyperbolic systems.

This talk will demonstrate a new closure technique that yields a set of fourteen moment equations that are robust, affordable, and mitigate spurious solution discontinuities.  This closure is inspired by the maximum-entropy closures, but avoids computational costs associated with the solution of the entropy maximization problem through a fitting technique.  The resulting first-order moment equations are easily amenable to solution using standard numerical mthods for hyperbolic problems.  A singularity in the flux vector, maintained from the maximum-entropy system, eliminates spurious discontinuities (sub-shocks) from high-speed-flow solutions.  One- and two-dimensional flow solutions are demonstrated.