A Novel Stagnation Streamline Model for Discrete-Velocity Simulation of Hypersonic Flows

Simulation of rarefied flow around a hypersonic vehicle necessitates the use of kinetic simulation tools, as continuum assumptions break down and computational fluid dynamics cannot be used. Discrete-velocity methods, which numerically solve the Boltzmann-BGK equations for a discretized velocity distribution function (VDF) at every point in the domain, are capable of capturing flow behavior without the statistical noise associated with conventional particle-based methods such as Direct Simulation Monte Carlo. However, the computational cost associated with discretizing both configuration and velocity space can be prohibitively expensive, making two or three dimensional simulations challenging. This paper presents the verification and benchmarking of a one-dimensional stagnation streamline model for discrete-velocity methods. The one-dimensional setup allows for efficient simulation of hypersonic flow behavior independent of vehicle design. Implementation procedures are described for the standard discrete-velocity method as well as the discrete-velocity method with the Parallel Kinetic Perpendicular Moments (PKPM) model: a simplification of the discrete-velocity scheme which assumes the perpendicular components of the VDF are Maxwellian while retaining non-equilibrium behavior in the parallel direction. Benchmarking results of the discrete-velocity stagnation streamline model against its Direct Simulation Monte Carlo equivalent demonstrate strong agreement. An analysis of the VDFs throughout the stagnation streamline is also performed to assess changing degrees of continuum behavior in transitional flowfields.