Learning Temporally Consistent Turbulence Between Sparse Snapshots via Diffusion Models
This provides a generative surrogate for turbulence modeling, which is incremental as it applies existing diffusion models to a specific fluid dynamics challenge.
The paper tackles the problem of reconstructing coherent turbulent dynamics between sparse snapshots of flow fields using conditional Denoising Diffusion Probabilistic Models, demonstrating the method on 2D Kolmogorov Flow and 3D Kelvin-Helmholtz Instability with analysis of statistical accuracy through metrics like turbulent kinetic energy spectra and temporal decay.
We investigate the statistical accuracy of temporally interpolated spatiotemporal flow sequences between sparse, decorrelated snapshots of turbulent flow fields using conditional Denoising Diffusion Probabilistic Models (DDPMs). The developed method is presented as a proof-of-concept generative surrogate for reconstructing coherent turbulent dynamics between sparse snapshots, demonstrated on a 2D Kolmogorov Flow, and a 3D Kelvin-Helmholtz Instability (KHI). We analyse the generated flow sequences through the lens of statistical turbulence, examining the time-averaged turbulent kinetic energy spectra over generated sequences, and temporal decay of turbulent structures. For the non-stationary Kelvin-Helmholtz Instability, we assess the ability of the proposed method to capture evolving flow statistics across the most strongly time-varying flow regime. We additionally examine instantaneous fields and physically motivated metrics at key stages of the KHI flow evolution.