Discrete-Velocity Simulation of One-Dimensional Hypersonic Stagnation Streamline

As a hypersonic vehicle increases in altitude, the validity of the continuum Navier–Stokes equations breaks down. Kinetic simulation tools, such as Direct Simulation Monte Carlo or discrete-velocity methods, make no assumptions of continuum behavior, allowing for accurate capture of gas dynamics in any regime. Although multidimensional simulations are ultimately required for vehicle design, one-dimensional analyses can be advantageous for investigating detailed flow physics independent of vehicle geometry. A framework exists for modeling a one-dimensional stagnation streamline in Direct Simulation Monte Carlo: as flow enters the domain, downstream particles are probabilistically removed according to conservation laws to obtain a steady state flow. This work derives the exact particle distribution function of removed particles so that the stagnation streamline framework can be implemented in discrete-velocity solvers. The discrete-velocity model is verified with a series of test problems and benchmarked against its Direct Simulation Monte Carlo equivalent. Strong agreement is achieved in terms of macroscopic and microscopic properties, including the velocity distribution function. The velocity distribution function analysis reveals features unique to a shock wave in the presence of a reflecting boundary. Guidelines for implementation of the stagnation streamline model for both codes are outlined.