Direct molecular gas dynamics simulations of re-entry vehicles via the Boltzmann equation

Abstract

This work explores the feasibility of performing three-dimensional molecular gas dynamics simulations of hypersonic flows such as re-entry vehicles through directly solving the six-dimensional nonlinear Boltzmann equation closed with the BGK (Bhatnagar-Gross-Krook) collision model. Through the combination of high-order unstructured spatial discretizations and conservative discrete velocity models as well as their efficient implementation on large-scale GPU computing architectures, we demonstrate the ability to simulate unsteady and non-equilibrium three-dimensional high-speed flows at a feasible computational cost through a unified numerical framework. We present the results of high-order simulations of the Apollo capsule at realistic re-entry conditions from the AS-202 mission flight path, including the steady non-equilibrium flow in the high-altitude regime at a Mach number of 22.7 and a Reynolds number of 43,000 as well as the unsteady turbulent flow in the low-altitude regime at a Mach number of 8 and a Reynolds number of 550,000. The results show the validity of the approach over the entire range of a typical re-entry trajectory from the rarefied to the continuum limit, the ability to directly resolve strong shocks profiles without numerical shock capturing techniques, and the ability of resolving small-scale unsteady flow structures in the inertial range.