Generalizable turbulence closures across bluff-body shapes by PINN-based solver-agnostic training

Abstract

Data-driven turbulence closures are usually calibrated by inverse methods that embed a CFD solver in the loop, tying the model to a particular discretization and requiring every iterate to yield a convergent solve. We instead train the closure inside a physics-informed neural network (PINN): the Reynolds-averaged Navier-Stokes residual is imposed by automatic differentiation, so the inverse problem is mesh-free, differentiable, and solver-agnostic. Because no forward solve runs during training, only the final closure need be solver-stable, arbitrary neural closures are admitted without an adjoint, and the iterative cost of adjoint or ensemble methods vanishes; each hypothesis trains in minutes on a single GPU, so the framework rapidly screens closure forms. We develop four closures: three model the Reynolds stress on a realizable tensor basis -- a local map, a non-local model transporting the turbulent kinetic energy and recovering the out-of-plane normal stress, and the same with a learned length scale l -- and a fourth models the Reynolds force F = -\nabla \cdot \tau directly, free of the realizability constraint. All four are trained across six two-dimensional bluff-body wakes at Re = 10^4 and deployed frozen in a standard finite-element solver, stabilized by input-gradient smoothing and a Lipschitz constraint. Under a strict leave-one-shape-out (LOSO) protocol, all four improve substantially on a steady SST k-omega baseline. The learned-length-scale closure is most accurate on the stress fields, while the force model generalizes best on the mean velocity and drag (LOSO drag error ~8.5%). The closures also train efficiently on Particle Image Velocimetry data, enabling geometries intractable for DNS.