Evaluations of large language models in computational fluid dynamics: Leveraging, learning and creating knowledge

This paper investigates the capabilities of large language models (LLMs) to leverage, learn and create knowledge in solving computational fluid dynamics (CFD) problems through three categories of baseline problems. These categories include (1) conventional CFD problems that can be solved using existing numerical methods in LLMs, such as lid-driven cavity flow and the Sod shock tube problem; (2) problems that require new numerical methods beyond those available in LLMs, such as the recently developed Chien-physics-informed neural networks for singularly perturbed convection–diffusion equations; and (3) problems that cannot be solved using existing numerical methods in LLMs, such as the ill-conditioned Hilbert linear algebraic systems. The evaluations indicate that reasoning LLMs overall outperform non-reasoning models in four test cases. Reasoning LLMs show excellent performance for CFD problems according to the tailored prompts, but their current capability in autonomous knowledge exploration and creation needs to be enhanced.