Physics-Based Machine Learning Closures and Wall Models for Hypersonic Transition-Continuum Boundary Layer Predictions

2025-07-11

AI Summary

In hypersonic transitional–continuum flows, the Navier–Stokes–Fourier equations coupled with empirical slip boundary conditions fail to accurately predict velocity slip, temperature jump, and shock structure due to breakdown of continuum assumptions. Method: This work proposes a physics-constrained machine learning framework comprising: (1) a physically interpretable wall model based on skewed Gaussian distributions, replacing empirical slip laws; (2) coupling of trace-free anisotropic viscosity with a physics-informed neural network that embeds governing PDEs and jointly learns stress and heat flux via adjoint-based optimization; and (3) multi-Knudsen-number parallel training with high-Mach data augmentation to enhance generalizability. Results: Validated on two-dimensional hypersonic flat-plate flow, the method significantly improves prediction accuracy of non-equilibrium effects—especially under high-Mach and high-Knudsen regimes—demonstrating the efficacy of physics-consistent, data-driven modeling for rarefied gas dynamics.

Technology Category

• Machine Learning: Hardware-aware ML
• Computer Vision: Low Level & Physics-based Vision
• Humans and AI: Human-in-the-loop Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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 (NSF) models with empirical slip-wall boundary conditions fail to accurately predict nonequilibrium effects such as velocity slip, temperature jump, and shock structure deviations. We develop a physics-constrained machine learning framework that augments transport models and boundary conditions to extend the applicability of continuum solvers in nonequilibrium hypersonic regimes. We employ deep learning PDE models (DPMs) for the viscous stress and heat flux embedded in the governing PDEs and trained via adjoint-based optimization. We evaluate these for two-dimensional supersonic flat-plate flows 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, particularly at high-Mach and high-Knudsen number regimes. Strategies such as parallel training across multiple Knudsen numbers and inclusion of high-Mach 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. This work establishes data-driven, physics-consistent strategies for improving hypersonic flow modeling for regimes in which conventional continuum approaches are invalid.

Problem

• Model rarefied hypersonic flows in transition-continuum regimes
• Improve accuracy of nonequilibrium effects prediction in hypersonic flows
• Develop physics-constrained machine learning for continuum solvers

Innovation

• Physics-constrained machine learning for hypersonic flows
• Deep learning PDE models for viscous stress
• Skewed-Gaussian wall model replaces empirical conditions