On Singular Closures for the 5-Moment System in Kinetic Gas Theory (Communications in Computational Physics, 2020)
Moment equations provide a flexible framework for the approximation ofthe Boltzmann equation in kinetic gas theory. While moments up to second order aresufficient for the description of equilibrium processes, the inclusion of higher ordermoments, such as the heat flux vector, extends the validity of the Euler equations tonon-equilibrium gas flows in a natural way.Unfortunately, the classical closure theory proposed by Grad leads to momentequations, which not only suffer from a restricted hyperbolicity region but are alsoaffected by non-physical sub-shocks in the continuous shock-structure problem if theshock velocity exceeds a critical value. A more recently suggested closure theory basedon the maximum entropy principle yields symmetric hyperbolic moment equations.However, if moments higher than second order are included, the computational demandof this closure can be overwhelming. Additionally, it was shown for the 5-moment system that the closing flux becomes singular on a subset of moments includingthe equilibrium state.Motivated by recent promising results of closed-form, singular closures based onthe maximum entropy approach, we study regularized singular closures that becomesingular on a subset of moments when the regularizing terms are removed. In orderto study some implications of singular closures, we use a recently proposed explicitclosure for the 5-moment equations. We show that this closure theory results in ahyperbolic system that can mitigate the problem of sub-shocks independent of theshock wave velocity and handle strongly non-equilibrium gas flows.