Symmetry aware Reynolds Averaged Navier Stokes turbulence models with equivariant neural networks
This work addresses the challenge of improving turbulence modeling in fluid dynamics for applications like aerodynamics and engineering simulations, offering a novel method for enforcing physical symmetries, though it builds on existing frameworks like structure tensors and rapid distortion theory.
The paper tackled the problem of developing accurate and generalizable Reynolds-averaged Navier-Stokes (RANS) models for turbulent flows by introducing symmetry-aware closures using equivariant neural networks (ENNs) and an algorithm for enforcing tensor contraction relations. The result showed that ENNs effectively learn high-order tensor relationships, meeting or exceeding existing models in tasks like predicting the rapid pressure-strain correlation, providing a physically consistent alternative to classical methods.
Accurate and generalizable Reynolds-averaged Navier-Stokes (RANS) models for turbulent flows rely on effective closures. We introduce tensor-based, symmetry aware closures using equivariant neural networks (ENNs) and present an algorithm for enforcing algebraic contraction relations among tensor components. The modeling approach builds on the structure tensor framework introduced by Kassinos and Reynolds to learn closures in the rapid distortion theory setting. Experiments show that ENNs can effectively learn relationships involving high-order tensors, meeting or exceeding the performance of existing models in tasks such as predicting the rapid pressure-strain correlation. Our results show that ENNs provide a physically consistent alternative to classical tensor basis models, enabling end-to-end learning of unclosed terms in RANS and fast exploration of model dependencies.