Large Language Model Driven Development of Turbulence Models

TL;DR

This work demonstrates a closed-loop, AI-assisted procedure in which an open-weight large language model (DeepSeek-R1) jointly develops near-wall turbulence closures for wall-modeled LES under adverse pressure gradients, spanwise rotation, and rough walls. The LLM collaborates with a fluids engineer, producing interpretable model formulations that are evaluated in CFD both a priori and a posteriori, iterating until fidelity to DNS references is achieved. The APG closure uses a thin-boundary-layer formulation with a material-derivative and pressure-gradient effects, the rotation closure modifies the law of the wall to include rotation corrections, and the rough-wall closure leverages an ANN-parameterized roughness function; in all cases, the LLM-derived closures outperform the conventional equilibrium wall model in canonical channel test cases. This study offers a proof-of-concept for AI-driven, interpretable scientific discovery in fluid mechanics and highlights both the potential and current limitations of open-weight LLMs for physics-based model development.

Abstract

Artificial intelligence (AI) has achieved human-level performance in specialized tasks such as Go, image recognition, and protein folding, raising the prospect of an AI singularity-where machines not only match but surpass human reasoning. Here, we demonstrate a step toward this vision in the context of turbulence modeling. By treating a large language model (LLM), DeepSeek-R1, as an equal partner, we establish a closed-loop, iterative workflow in which the LLM proposes, refines, and reasons about near-wall turbulence models under adverse pressure gradients (APGs), system rotation, and surface roughness. Through multiple rounds of interaction involving long-chain reasoning and a priori and a posteriori evaluations, the LLM generates models that not only rediscover established strategies but also synthesize new ones that outperform baseline wall models. Specifically, it recommends incorporating a material derivative to capture history effects in APG flows, modifying the law of the wall to account for system rotation, and developing rough-wall models informed by surface statistics. In contrast to conventional data-driven turbulence modeling-often characterized by human-designed, black-box architectures-the models developed here are physically interpretable and grounded in clear reasoning.

Figures (7)

• Figure 1: (a) Schematic of wall-modeled LES (WMLES). A wall model predicts the wall fluxes—shear stress $\tau_w$ and heat flux $q_w$—based on LES-resolved flow quantities at a distance $h_{\rm wm}$ from the wall. (b) Blades in a turbine, illustrating flows subjected non-equilibrium effects such as APGs ( red box), system rotation ( orange box), and surface roughness ( purple box). (c) Model problems. From left to righ: channel subjected a suddenly imposed APG, channel with system rotation, and channel with rough on the bottom wall.
• Figure 2: Schematic overview of the interaction between the LLM and the user for the APG modeling problem.
• Figure 3: (a-c) Inner-scaled mean velocity profiles following the imposition of an APG: (a) R5APG1; (b) R5APG100; (c) R10APG100. Time $T$ is normalized by $h/U_{c,0}$, where $U_{c,0}$ is the channel centerline velocity at $t=0$. (d-f) Evolution of the wall shear stress: (d) R5APG1; (e) R5APG100; (f) R10APG100. The dashed line corresponds to the results fo the EWM. DNS reference data are shown in color, and predictions from the model in Eq. \ref{['eq:A22']} are labeled 'DS-C1'.
• Figure 4: Schematic overview of the interaction between the LLM and the user for the spanwise rotation modeling problem.
• Figure 5: Mean velocity profiles in spanwise rotating channels. (a) R2ROT10; (b) R2ROT120; (c) R4ROT20; (d) R4ROT32. Label 'DS-C2' corresponds to the model in Eq. \ref{['eq:B11']}.