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Generative Reconstruction of Spatiotemporal Wall-Pressure in Turbulent Boundary Layers via Patchwise Latent Diffusion

Xiantao Fan, Meet Hemant Parikh, Yi Liu, Xin-Yang Liu, Junyi Guo, Meng Wang, Jian-Xun Wang

TL;DR

This work tackles reconstructing the full spatiotemporal wall-pressure field $p_w(x,z,t)$ in turbulent boundary layers from sparse surface measurements, acknowledging the nonlocal Poisson coupling that governs pressure. It introduces a two-stage generative framework that couples a domain-decomposed conditional neural field (D-CNF) for local, high-resolution latent representations with a patchwise latent diffusion model, enabling zero-shot adaptation to sensor layouts and varying pressure-gradient regimes via diffusion posterior sampling (DPS) and classifier-free guidance (CFG). The approach yields ensembles with calibrated uncertainty and demonstrates high-fidelity instantaneous reconstructions and preserved statistics (PDFs, spectra, space-time correlations, convection velocity) across ZPG, APG, and FPG conditions, while offering substantial runtime advantages over DNS-based inverse methods. This framework provides a practical, scalable surrogate for design and control tasks requiring spatiotemporal wall-pressure fields under sparse sensing, with clear paths for reducing seam artifacts and accelerating inference in future work.

Abstract

Wall-pressure fluctuations in turbulent boundary layers drive flow-induced noise, structural vibration, and hydroacoustic disturbances, especially in underwater and aerospace systems. Accurate prediction of their wavenumber-frequency spectra is critical for mitigation and design, yet empirical/analytical models rely on simplifying assumptions and miss the full spatiotemporal complexity, while high-fidelity simulations are prohibitive at high Reynolds numbers. Experimental measurements, though accessible, typically provide only pointwise signals and lack the resolution to recover full spatiotemporal fields. We propose a probabilistic generative framework that couples a patchwise (domain-decomposed) conditional neural field with a latent diffusion model to synthesize spatiotemporal wall-pressure fields under varying pressure-gradient conditions. The model conditions on sparse surface-sensor measurements and a low-cost mean-pressure descriptor, supports zero-shot adaptation to new sensor layouts, and produces ensembles with calibrated uncertainty. Validation against reference data shows accurate recovery of instantaneous fields and key statistics.

Generative Reconstruction of Spatiotemporal Wall-Pressure in Turbulent Boundary Layers via Patchwise Latent Diffusion

TL;DR

This work tackles reconstructing the full spatiotemporal wall-pressure field in turbulent boundary layers from sparse surface measurements, acknowledging the nonlocal Poisson coupling that governs pressure. It introduces a two-stage generative framework that couples a domain-decomposed conditional neural field (D-CNF) for local, high-resolution latent representations with a patchwise latent diffusion model, enabling zero-shot adaptation to sensor layouts and varying pressure-gradient regimes via diffusion posterior sampling (DPS) and classifier-free guidance (CFG). The approach yields ensembles with calibrated uncertainty and demonstrates high-fidelity instantaneous reconstructions and preserved statistics (PDFs, spectra, space-time correlations, convection velocity) across ZPG, APG, and FPG conditions, while offering substantial runtime advantages over DNS-based inverse methods. This framework provides a practical, scalable surrogate for design and control tasks requiring spatiotemporal wall-pressure fields under sparse sensing, with clear paths for reducing seam artifacts and accelerating inference in future work.

Abstract

Wall-pressure fluctuations in turbulent boundary layers drive flow-induced noise, structural vibration, and hydroacoustic disturbances, especially in underwater and aerospace systems. Accurate prediction of their wavenumber-frequency spectra is critical for mitigation and design, yet empirical/analytical models rely on simplifying assumptions and miss the full spatiotemporal complexity, while high-fidelity simulations are prohibitive at high Reynolds numbers. Experimental measurements, though accessible, typically provide only pointwise signals and lack the resolution to recover full spatiotemporal fields. We propose a probabilistic generative framework that couples a patchwise (domain-decomposed) conditional neural field with a latent diffusion model to synthesize spatiotemporal wall-pressure fields under varying pressure-gradient conditions. The model conditions on sparse surface-sensor measurements and a low-cost mean-pressure descriptor, supports zero-shot adaptation to new sensor layouts, and produces ensembles with calibrated uncertainty. Validation against reference data shows accurate recovery of instantaneous fields and key statistics.

Paper Structure

This paper contains 19 sections, 16 equations, 38 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Problem formulation
  4. Domain-decomposed conditional neural field for latent representation
  5. Conditional latent diffusion model with classifier-free guidance
  6. Generative reconstruction from sparse wall measurements without retraining
  7. Results
  8. Case setup and training data generation
  9. Generative wall-pressure reconstruction (single-regime testing)
  10. Generative wall-pressure reconstruction under different pressure gradients (cross-regime testing)
  11. Computational cost (forward vs. inverse)
  12. Discussion
  13. Generalizability of the domain-decomposed CNF
  14. Analysis of diffusion-generated latents
  15. Novelty, limitation and future prospects
  16. ...and 4 more sections

Figures (38)

  • Figure 1: Schematic of the generative framework for reconstructing wall pressure. Top: the domain-decomposed conditional neural field (D-CNF) encodes the physical domain into latent space and decodes latents back to fields. Bottom: the latent diffusion model with two conditioning mechanisms: (I) sensor consistency via DPS (inference only) and (II) flow-regime guidance via a mean-profile descriptor used in both training and inference. Solid arrows denote training; dashed arrows denote inference.
  • Figure 2: Dataset validation: (a) Mean velocity and (b) velocity fluctuations at the inlet, compared with DNS data from spalart1988direct; (c) Skin friction and (d) mean pressure coefficient for a turbulent boundary layer under strong APG/FPG (V90, $\beta = 90.19$), compared with DNS results from abe2017reynolds. Reference data are shown as scatter points, while our results are plotted as lines.
  • Figure 3: Reconstructed wall-pressure fluctuations for Case V0 (ZPG, $\beta = 0$), conditioned on sensor arrays at unseen time steps.
  • Figure 4: Reconstructed wall-pressure fluctuations for Case V40 (APG/FPG, $\beta = 6.92$), conditioned on sensor arrays at unseen time steps
  • Figure 5: Reconstructed wall-pressure fluctuations for Case V80 (APG/FPG, $\beta = 62.31$), conditioned on sensor arrays at unseen time steps
  • ...and 33 more figures