Seminars

The goal of the work presented is to develop an accurate and efficient flow solver based upon a discrete velocity description of the Boltzmann equation. Continuum equations fail to accurately represent a flow when mean free paths are on the same order as the characteristic length scale, and the Boltzmann equation must be solved instead. This condition may occur in micro- and nano-scale devices, shocks, satellite attitude control thruster plumes, around satellites in low-earth orbit, and during hypersonic re-entry.

Standard particle based methods such as direct simulation Monte Carlo (DSMC) have difficulties with complex and transient flows, and the high noise associated with simulations under these conditions can create problems when coupling with continuum solvers and can wash out changes to the properties of trace species. To address these issues, a discrete velocity method (DVM) was developed which models the evolution of a flow through the collisions and motion of fixed velocity, variable mass quasi-particles defined as delta functions on a truncated and discretized velocity domain.

The work is an extension of a previous method developed for a single, monatomic species solved on a uniform (evenly spaced) velocity grid with either a hard sphere or pseudo-Maxwell collision cross-section model. The collision integral is solved with a variance reduced stochastic model where the deviation from equilibrium is calculated and operated upon. This method produces fast, smooth solutions of near-equilibrium flows. In the current work, advancements were made in the following areas: implementation of variable hard sphere and variable soft sphere collision models, diffuse boundary conditions, non-uniform (realigned) grids, multi-species, and quantized rotational and vibrational energy. Each advancement to the method was accompanied by an equivalent extension of the variance reduction collision model in order to maintain the benefits of low noise and fast solutions.