Kinetic algorithms for nonequilibrium gas dynamics

New upwind kinetic-difference schemes have been developed for flows with non-equilibrium thermodynamics and chemistry. These schemes are derived from the Boltzmann equation with the resulting Euler schemes developed as moments of the discretized Boltzmann scheme with a locally Maxwellian velocity distribution. Application of a directionally-split Courant-Isaacson-Rees (CIR) scheme at the Boltzmann level results in a flux-vector splitting scheme at the Euler level and is called Kinetic Flux-Vector Splitting (KFVS). Computational examples are presented comparing KFVS with the schemes of Van-Leer and Roe for quasi-one-dimensional flow through a supersonic diffuser, inviscid flow through two-dimensional inlet, viscous flow over a cone at zero angle-of-attack, and shock-induced combustion/detonation in a premixed hydrogen-air mixture. The results show that even though the KFVS scheme is a Riemann solver at the kinetic level, its behavior at the Euler level is more similar to the existing flux-vector splitting algorithms than to the flux-difference splitting scheme of Roe.; A new approach toward the development of a genuinely multi-dimensional Riemann solver is also presented. The approach taken in the present work is to apply new multi-dimensional upwind schemes for the scalar advection equation at the Boltzmann level. The resulting Euler schemes are obtained as moments of the fluctuations in the Maxwellian distribution function. The theoretical issues have been solved through analytic quadrature and Euler schemes have been developed. Encouraging preliminary results have been obtained for perfect gases on uniform Cartesian meshes with first-order spatial accuracy.; Finally, methods for obtaining accurate gas-dynamic simulations in the continuum transition regime are considered. In particular, large departures from translational equilibrium are modeled using algorithms based on the Burnett equations instead of the Navier-Stokes equations. Here, the same continuum formulation of the governing equations is retained, but new constitutive relations based on higher-order Chapman-Enskog theory are introduced. Both a rotational relaxation model and a bulk-viscosity model have been considered for simulating rotational non-equilibrium. Results are presented for hypersonic normal shock calculations in argon and diatomic nitrogen and comparisons are made with Direct Simulation Monte Carlo (DSMC) results. (Abstract shortened by UMI.)...