Hyperbolic Moment Equations in Kinetic Gas Theory Based on Multi-Variate Pearson-IV-Distributions (Communications in Computational Physics, 2010)
In this paper we develop a new closure theory for moment approximationsin kinetic gas theory and derive hyperbolic moment equations for 13 fluid variablesincluding stress and heat flux. Classical equations have either restricted hyperbolicityregions like Grad's moment equations or fail to include higher moments in apractical way like the entropy maximization approach. The new closure is based onPearson-Type-IV distributions which reduce to Maxwellians in equilibrium, but allowanisotropies and skewness in non-equilibrium. The closure relations are essentiallyexplicit and easy to evaluate. Hyperbolicity is shown numerically for a large range ofvalues. Numerical solutions of Riemann problems demonstrate the capability of thenew equations to handle strong non-equilibrium.