AeroDiT: Diffusion Transformers for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows

Abstract

Real-time and accurate prediction of aerodynamic flow fields around airfoils is crucial for flow control and aerodynamic optimization. However, achieving this remains challenging due to the high computational costs and the non-linear nature of flow physics. Traditional Computational Fluid Dynamics (CFD) methods face limitations in balancing computational efficiency and accuracy, hindering their application in real-time scenarios. To address these challenges, this study presents AeroDiT, a novel surrogate model that integrates scalable diffusion models with transformer architectures to address these challenges. Trained on Reynolds-Averaged Navier-Stokes (RANS) simulation data for high Reynolds-number airfoil flows, AeroDiT accurately captures complex flow patterns while enabling real-time predictions. The model demonstrates impressive performance, with mean relative $L_2$ errors of 0.1, 0.025, and 0.050 for pressure $p$ and velocity components $u_x, u_y$, confirming its reliability. To further enhance physical consistency, we incorporate explicit physics-informed losses based on RANS residuals, including mass and momentum conservation constraints. The transformer-based structure allows for real-time predictions within seconds, enabling efficient aerodynamic simulations. This work underscores the potential of generative machine learning techniques to advance computational fluid dynamics, offering potential solutions to challenges in simulating high-fidelity aerodynamic flows.

Figures (11)

• Figure 1: Overview of the AeroDiT framework. The input consists of three channels: airfoil geometry mask, horizontal velocity ($u_x$), and vertical velocity ($u_y$), concatenated as a tensor of shape $[B, 3, H, W]$. These are processed by the Condition Encoder, which downsamples the input into a latent representation. Simultaneously, the ground truth pressure and velocity fields are encoded into a target latent space by a VAE. The Diffusion Transformer (DiT) operates on this latent space by iteratively denoising the noisy latent using transformer blocks conditioned on the encoded input and timestep embeddings. The output latent is decoded by the Function Space Decoder to reconstruct the pressure and velocity fields. The model is optimized using a combination of data loss, mass conservation loss, and momentum conservation loss to ensure physical consistency.
• Figure 2: Illustration of the forward and backward diffusion process.
• Figure 3: Wing geometry. (The red part shows the wing and the blue part shows the flow field)
• Figure 4: Visualization of input data (Airfoil geometry, initial horizontal velocity, initial parallel velocity), prediction (Pressure Field, velocity X, velocity Y) and the corresponding ground truth.
• Figure 5: Further studies on AeroDiT training and inference process.