用扩散模型从顶层数据重建高超音速边界层,保持细节和不确定性。
Multiscale Hypersonic Boundary Layer Reconstruction via Spectral Binning and Subdomain-wise Conditional Diffusion

- 分层建模+条件扩散,从顶层观测推断壁面状态
- 恢复真实速度/温度场结构,频谱精度提升且数值稳定
- 适合高超音速湍流研究者,提供物理一致的不确定性
本文提出一种多尺度概率重建框架,用于高超音速耦埃特流动。通过条件扩散模型,基于有限的顶壁观测推断近壁状态。将边界层划分为重叠的壁法向子域,联合训练一个针对M=6、7、8的、高度与马赫数条件化的阐明性扩散模型(EDM),以生成速度、密度、压力和温度场。采用软重叠修补策略融合子域预测,确保域间连续性和小尺度波动。为提升生成场的频谱保真度,引入新型有界分箱谱功率(BSP)损失,在扩散噪声调度下保持高波数成分并保证数值稳定。与直接数值模拟数据对比表明,该模型能准确恢复瞬时结构、频谱、统计剖面、相关性及壁面量,同时提供空间结构化的不确定性估计。重构的马赫条件剖面在Trettel-Larsson变换下实现自洽,符合压缩性标度规律。结果证明,结合有界分箱谱损失的域分解条件扩散模型是高超音速壁湍流近壁重建的有效概率代理。
原文摘要 · Abstract (English)
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.
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