Title page for ETD etd-06062008-165605
|Type of Document
||Eppard, William M.
||Kinetic algorithms for non-equilibrium gas dynamics
|Grossman, Bernard M.
|Jakubowski, Antoni K.
|Mason, William H.
|Schetz, Joseph A.
|Walters, Robert W.
|Date of Defense
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.
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