Seminars

The thermal non-equilibrium flow regime is characterized by flows where the mean free path is of the same order or greater than the characteristic length scale for macroscopic gradients. The Navier-Stokes (continuum) equations fail to accurately represent flow under the conditions described, and different equations that remove the continuum constraint and model the gas on a macroscopic level are needed. The Boltzmann equation describes the behavior of a gas in thermal non-equilibrium and is used when the Navier-Stokes equations fail. A discrete velocity (DV) method for solving the Boltzmann equation has been developed where the velocity domain is truncated and discretized into a finite set of grid points. Collisions are modeled using a stochastic Monte Carlo based method called variance reduction where the deviation from equilibrium is used to calculate the collision integral instead of the total velocity distribution function. Variance reduction allows for smoother and faster solutions than comparative stochastic schemes. The method has been extended to include various collision cross-section models (variable hard sphere and variable soft sphere), gas mixtures with large mass ratios and/or trace species, and diatomic molecules with rotational and vibrational energy. Internal energy is described using a quantum model, and the energy exchanges between modes are approximated by drawing post-collision energy levels from an equilibrium Boltzmann distribution defined by the collision energy.