  This work explores the capability of simulating complex fluid flows by
directly solving the Boltzmann equation. Due to the high-dimensionality of the
governing equation, the substantial computational cost of solving the Boltzmann
equation has generally limited its application to simpler, two-dimensional flow
problems. Utilizing a combination of high-order spatial discretizations and
discretely-conservative velocity models along with their highly-efficient
implementation on massively-parallel GPU computing architectures, we
demonstrate the current ability of directly solving the Boltzmann equation
augmented with the BGK collision model for complex, three-dimensional flows.
Numerical results are presented for a variety of these problems including
rarefied microchannels, transitional and turbulent flows, and high-speed
atmospheric re-entry vehicles, showcasing the ability of the approach in
accurately predicting complex nonlinear flow phenomena and non-equilibrium
effects.
