Kinetic algorithms for non-equilibrium gas dynamics
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New upwind kinetic-difference schemes have been developed for flows with nonequilibrium 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). Extension to flows with finite-rate chemistry and vibrational relaxation is accomplished utilizing non-equilibrium kinetic theory. 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 angleof- attack, and shock-induced combustion/detonation in a premixed hydrogen-air mixture. Calculations are also shown for the transonic flow over a bump in a channel and the transonic flow over an NACA 0012 airfoil. 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 the existing flux-vector splitting algorithms than to the flux-difference splitting scheme of Roe.
- Doctoral Dissertations