Affordable Extended Hyperbolic Moment Closures for Rarefied Gas-Flow Predictions

Abstract

For the past 75 years, moment closures have been a promising method of gas-flow prediction for rarefied gases, as they offer significant mathematical and computational advantages over other applicable methods in regimes outside of local thermodynamic equilibrium. However, many of these advantages come from their ability to be formulated as hyperbolic systems of balance laws. Only recently have there been generalizable hyperbolic closures which can be expressed in closed form, and many of these closures have been restricted to simplified one-dimensional gases. While mathematically elegant, this limits the practical use of these new hierarchies to academic problems. Extending their desirable mathematical properties to real multidimensional gases has proven difficult, and a new method to handle this extension is the goal of this thesis. First, existing hierarchies of moment closures are presented, as well as their mathematical properties. Next, the technique by which higher-order moment models can be constructed is presented, with two new 20-moment closures being developed as a result. Linear stability of these models is presented, along with their performance in canonical discontinuous gas-flow problems for the continuum, transition, and free-molecular flow regimes. The traditional formulation of boundary conditions in kinetic theory is difficult to replicate in this framework. Instead, a new formulation of the Knudsen-layer boundary condition is presented, with results for both the 10-moment and 20-moment equations in canonical boundary-value problems. Finally, results for more realistic gas-flow problems in rarefied settings are shown. Strong shocks, and flows with regions of large translational non-equilibrium, are also explored. Further possible extensions for the models, such as for diatomic gases and plasmas, conclude the thesis.