CoNFiLD-inlet: Synthetic Turbulence Inflow Using Generative Latent Diffusion Models with Neural Fields

TL;DR

CoNFiLD-inlet is presented, a novel DL-based inflow turbulence generator that integrates diffusion models with a conditional neural field (CNF)-encoded latent space to produce realistic, stochastic inflow turbulence.

Abstract

Eddy-resolving turbulence simulations require stochastic inflow conditions that accurately replicate the complex, multi-scale structures of turbulence. Traditional recycling-based methods rely on computationally expensive precursor simulations, while existing synthetic inflow generators often fail to reproduce realistic coherent structures of turbulence. Recent advances in deep learning (DL) have opened new possibilities for inflow turbulence generation, yet many DL-based methods rely on deterministic, autoregressive frameworks prone to error accumulation, resulting in poor robustness for long-term predictions. In this work, we present CoNFiLD-inlet, a novel DL-based inflow turbulence generator that integrates diffusion models with a conditional neural field (CNF)-encoded latent space to produce realistic, stochastic inflow turbulence. By parameterizing inflow conditions using Reynolds numbers, CoNFiLD-inlet generalizes effectively across a wide range of Reynolds numbers ($Re_τ$ between $10^3$ and $10^4$) without requiring retraining or parameter tuning. Comprehensive validation through a priori and a posteriori tests in Direct Numerical Simulation (DNS) and Wall-Modeled Large Eddy Simulation (WMLES) demonstrates its high fidelity, robustness, and scalability, positioning it as an efficient and versatile solution for inflow turbulence synthesis.

Figures (57)

• Figure 1: Overview of the proposed CoNFiLD-inlet model. The dashed lines denote the extra conditioning information (the mean velocity $\langle u\rangle(y)$) that can be provided to guide the conditional generation process.
• Figure 1: Statistical validation of the DNS training dataset. (a) Mean velocity profile, validated against the data from moser1999direct. (b) Turbulence intensity,compared with moser1999direct. (c) Root-mean-square values of pressure fluctuations, compared with kim1987turbulence. (d) Reynolds shear stress, compared with abe2001direct. (e) Energy spectra along streamwise direction and (f) spanwise direction, compared with rai1991direct. Solid lines represent the present simulation, while scatter points denote reference data.
• Figure 1: Statistics of a priori test of the $5$ random samples generate by CoNFiLD-inlet at $Re_\tau=5000$. Each sample is represented by one color while the reference data is marked by the black dashed line. Among them, we pick the visually best sample to report in the main test which is colored by orange. (a) Mean velocity profile. (b) Auto correlation $R_{11}$ at channel center. (c) Reynolds shear stress $\langle u'v'\rangle$. Turbulence intensity of $u$ (d) and $w$ (e). (f) Turbulence Kinetic Energy (TKE) along span wise wavenumber at channel center.
• Figure 1: Stretching mesh (a) versus the uniform mesh (b) for the DNS $\mathbb{I}$
• Figure 1: Two dimensional t-SNE visualization of the training data used in the DNS inlet generator. The velocity field at each time step is projected as one dot and the color indicates the time step.