[2511.09769] Structure tensor Reynolds-averaged Navier-Stokes turbulence models with equivariant neural networks

Physics > Fluid Dynamics arXiv:2511.09769 (physics) [Submitted on 12 Nov 2025 (v1), last revised 27 Feb 2026 (this version, v2)] Title:Structure tensor Reynolds-averaged Navier-Stokes turbulence models with equivariant neural networks Authors:Aaron Miller, Sahil Kommalapati, Robert Moser, Petros Koumoutsakos View a PDF of the paper titled Structure tensor Reynolds-averaged Navier-Stokes turbulence models with equivariant neural networks, by Aaron Miller and 3 other authors View PDF HTML (experimental) Abstract:Accurate and generalizable Reynolds-averaged Navier-Stokes (RANS) models for turbulent flows rely on effective closures, but currently available closures are notoriously unreliable. Kassinos et al. (J. Fluid Mechanics, 428, pp. 213-248, 2001) hypothesized that this unreliability of RANS models was due to an insufficient description of the statistical state of the turbulence and proposed a set of structure tensors as a candidate for a sufficiently rich description. To test this hypothesis for the rapid pressure-strain term, we introduce tensor-based, symmetry aware closures in terms of the structure tensors using equivariant neural networks (ENNs), and present an algorithm for enforcing algebraic contraction relations among tensor components. Using data from rapid distortion theory, experiments show that such ENNs can effectively learn relationships involving high-order tensors. The resulting ENN structure tensor models are orders of magnitude more accurate than exist...