Multiscale Hypersonic Boundary Layer Reconstruction via Spectral Binning and Subdomain-wise Conditional Diffusion

2026-06-12

AI Summary

This study addresses the challenge of reconstructing near-wall instantaneous flow fields in hypersonic Couette flow from sparse top-wall observational data by proposing a subdomain-decomposed conditional diffusion model framework. The boundary layer is partitioned into overlapping normal-direction subdomains, each processed by a unified diffusion model conditioned on both wall-normal height and Mach number, with predictions stitched together via a soft-overlap inpainting strategy. A novel bounded binned spectral power (BSP) loss function is introduced to preserve high-frequency content, complemented by Trettel–Larsson compressibility scaling analysis. This approach enables, for the first time, probabilistic reconstruction and spatially structured uncertainty quantification of hypersonic turbulent boundary layers across multiple Mach numbers, accurately reproducing instantaneous structures, energy spectra, statistical profiles, correlations, and wall quantities consistent with established compressibility scaling laws.

Abstract

We propose a multiscale probabilistic reconstruction framework for hypersonic Couette flow, where near-wall states are inferred from limited top-wall observations using conditional diffusion model. The boundary layer is divided into overlapping wall-normal subdomains, and a single height- and Mach-conditioned Elucidating Diffusion Model (EDM) is trained jointly for M=6,7,8 to sample velocity, density, pressure, and temperature fields conditioned on a top-wall boundary slice. A soft overlap inpainting strategy assembles subdomain predictions into full-volume reconstructions while maintaining inter-subdomain continuity and small-scale variability. To improve the spectral fidelity of the generated fields, we introduce a novel bounded binned spectral power (BSP) loss that preserves high-wavenumber content while remaining numerically stable across the diffusion noise schedule. Validation against direct numerical simulation data shows that the model recovers instantaneous structures, spectra, statistical profiles, correlations, and wall quantities across all training Mach numbers, while providing spatially structured uncertainty estimates. The reconstructed Mach-conditioned profiles also collapse under the Trettel-Larsson transformation, indicating consistency with compressibility scaling. These results establish the domain decomposed conditional diffusion model with a bounded binned spectral loss as an effective probabilistic surrogate for near-wall reconstruction in hypersonic wall-bounded turbulence.

Problem

• hypersonic boundary layer
• flow reconstruction
• conditional diffusion
• multiscale modeling
• wall-bounded turbulence

Innovation

• conditional diffusion model
• spectral binning
• subdomain decomposition
• hypersonic boundary layer
• bounded binned spectral loss