Data-Driven Extraction of 3D Orthogonal Velocity Distribution Modes from 1D DSMC Shocks

Abstract This work investigates the structure of 3D particle velocity distribution functions (VDFs) within 1D normal shock waves. To explore the potential to extend continuum Boltzmann reduced order models previously studied only for a subset of homogeneous relaxation problems, low-rank modal structures are extracted from normalized Mach 2 and Mach 8 shock structure solutions. Because full 1D shock structure solutions are not readily available, cell-based continuum VDFs are instead sampled from highly resolved Direct Simulation Monte Carlo (DSMC) results. Normalized heat fluxes for Mach 2 and Mach 8 shocks are compared with expansion in terms of the Sonine polynomials traditionally used in Chapman-Enskog expansions. The viability of adapting the resulting data-driven modes for development of spatially inhomogeneous Boltzmann-ROMs and potential for other future algorithmic hybridization are also discussed.