Data-driven transport and wall models for transition-continuum flows based on modeled distribution functions

Modeling hypersonic flows in the transition–continuum regime (0.1 < Kn < 10) is challenging because classical Navier–Stokes–Fourier (NSF) solvers with slip/jump boundary conditions fail to capture nonequilibrium effects, while high-fidelity kinetic methods such as those solving the Boltzmann equation (e.g., DSMC) are computationally expensive. We develop a physics-constrained machine learning (ML) framework that embeds neural network closures for viscous stress and heat flux into the governing equations and introduces a novel skewed-Gaussian distribution function wall model to replace empirical slip conditions. These models are trained using adjoint-based optimization on DSMC data for flat-plate boundary layers in argon across Mach numbers 3–12 and Knudsen numbers 0.3–1.2. The resulting trace-free anisotropic transport model and wall model improve velocity, temperature, heat flux, and viscous stress predictions, especially near the wall under strong rarefaction. The coupled models generalize well to out-of-sample Mach numbers, preserve thermodynamic consistency, and capture nonequilibrium boundary layer behavior at a fraction of the cost of Boltzmann equation-based methods, demonstrating a pathway to extend continuum solvers for hypersonic vehicle design.