From Zero to Turbulence: Generative Modeling for 3D Flow Simulation

TL;DR

The paper addresses the heavy computational cost of 3D turbulence CFD by proposing TurbDiff, a diffusion-based generative model that samples from the distribution of fully developed turbulent states without relying on an initial turbulent condition. By formulating generative turbulence simulation and coupling a 3D U-Net with a transformer under a DDPM framework, the authors demonstrate generalization to unseen geometries and introduce two distribution-focused metrics (TKE-based and region-based) to evaluate sample realism. Experimental results on a new high-resolution 3D turbulence dataset show TurbDiff produces high-fidelity samples with competitive distributional quality and over 30x faster sampling than full solvers, while autoregressive baselines struggle with long rollouts. The work provides practical impact for design optimization and turbulence analysis by enabling rapid, boundary-conditioned sampling of turbulent states, and it lays groundwork for geometry-generalizable generative turbulence models.

Abstract

Simulations of turbulent flows in 3D are one of the most expensive simulations in computational fluid dynamics (CFD). Many works have been written on surrogate models to replace numerical solvers for fluid flows with faster, learned, autoregressive models. However, the intricacies of turbulence in three dimensions necessitate training these models with very small time steps, while generating realistic flow states requires either long roll-outs with many steps and significant error accumulation or starting from a known, realistic flow state - something we aimed to avoid in the first place. Instead, we propose to approach turbulent flow simulation as a generative task directly learning the manifold of all possible turbulent flow states without relying on any initial flow state. For our experiments, we introduce a challenging 3D turbulence dataset of high-resolution flows and detailed vortex structures caused by various objects and derive two novel sample evaluation metrics for turbulent flows. On this dataset, we show that our generative model captures the distribution of turbulent flows caused by unseen objects and generates high-quality, realistic samples amenable for downstream applications without access to any initial state.

Figures (7)

• Figure 1: The same simulation exhibits vastly different qualities when the solver operates in three dimensions compared to two.
• Figure 2: 1-step forecast MSE of $u$ increases at a rate comparable to Gaussian smoothing of states to remove small-scale features.
• Figure 3: Error accumulates quickly for longer roll-outs even when the time step is sufficiently small.
• Figure 4: A subset of the objects in our turbulent flow dataset with isosurfaces of the vorticity magnitude.
• Figure 5: Example flows for a test object from our dataset showing isosurfaces of the vorticity ${\bm{\omega}}$.