Discrete Velocity Models for Mixtures and Non-Mixtures
Doctoral Thesis
This thesis explores the application of discrete velocity models (DVM) for simulating gas mixtures, providing an introduction to key theoretical results of both the continuous Boltzmann equation and DVM for mixtures. It derives closure terms for the Navier-Stokes equation from the continuous Boltzmann equation and presents efficient algorithms for setting up DVM in two or three-dimensional velocity spaces, significantly faster than naive implementations. This speed is crucial for mixtures, as different mass ratios often necessitate new DVM configurations. The work also addresses the optimal size of discrete velocity spaces, emphasizing the need for a balance in momentum and energy transfer between species, alongside supernormality. Insufficiently sized velocity grids can lead to inadequate energy transferring collisions, distorting relaxation processes. The thesis investigates suitable distributions for given velocity grids and develops a moment-based metric to determine optimal parameter ranges for temperature and mean velocity. Additionally, a generic method for automatically determining collision weights is introduced, allowing for sql-like grouping operations and adjustments to balance intra- and interspecies collisions. This approach is employed to mitigate discretization effects on viscosity and Prandtl number.
