Physics-based machine learning closures and wall models for hypersonic transition-continuum boundary layer predictions
Phys. Rev. Fluids 11, 033402 – Published 2 March, 2026
DOI: https://doi.org/10.1103/hxn8-75bb
Abstract
Modeling rarefied hypersonic flows remains a fundamental challenge due to the breakdown of classical continuum assumptions in the transition-continuum regime, where the Knudsen number ranges from approximately 0.1 to 10. Conventional Navier-Stokes-Fourier models with empirical slip-wall boundary conditions fail to accurately predict nonequilibrium effects such as velocity slip, temperature jump, and shock structure deviations. In this work, we develop a physics-constrained machine learning framework that augments bulk transport models and boundary conditions to extend the applicability of continuum solvers in nonequilibrium hypersonic regimes. We employ deep learning partial differential equation models for the viscous stress and heat flux embedded in the governing equations and trained via adjoint-based optimization. Three closure strategies are evaluated for two-dimensional supersonic flat-plate flows in argon across a range of Mach and Knudsen numbers. Additionally, we introduce a wall model based on a mixture of skewed Gaussian approximations of the particle velocity distribution function. This wall model replaces empirical slip conditions with physically informed, data-driven boundary conditions for the streamwise velocity and wall temperature. Our results show that a trace-free anisotropic viscosity model, paired with the skewed-Gaussian distribution function wall model, achieves significantly improved accuracy in predicting both bulk and wall quantities, particularly at high-Mach-number- and high-Knudsennumber regimes. Strategies such as parallel training across multiple Knudsen numbers and inclusion of high-Mach-number data during training are shown to enhance model generalization. Increasing model complexity yields diminishing returns for out-of-sample cases, underscoring the need to balance degrees of freedom and overfitting. To further assess generalization, we test the best-performing model on a geometrically out-of-sample wedge with increasing wall angles, for which the accuracy of the augmented predictions is consistent with the deviation from the training configuration. This work establishes data-driven, physics-consistent strategies for improving hypersonic flow modeling for regimes in which conventional continuum approaches are invalid.
