2026/07/22 by Jiaqi Li, Robert F. Kunz, George Huang +1
#physics.flu-dyn
In fluid engineering, the turbulence problem is the longstanding challenge of obtaining accurate predictions of engineering quantities at affordable computational cost. Viewed through computational complexity, a practical algorithm requires cost growth no worse than O(N), where N denotes problem size. For turbulent flows, the problem size may be approximated by the number of dynamically relevant scales and hence by the Reynolds number Re. We propose a multi-fidelity, physics-constrained, data-driven framework designed to meet this criterion under stated assumptions. We augment the Spalart--Allmaras model through field inversion and machine learning using a constrained formulation that preserves the law of the wall. The model is trained at a low Reynolds number, where high-fidelity data are affordable, and deployed at higher Reynolds numbers. For a mean-flow-aligned grid in a wall-bounded flow, fixed spanwise resolution, and steady-solver cost linear in grid-point count, the low-fidelity RANS prediction scales as O(log(Re)). The high-fidelity calculation and learning stage each contribute O(Re0) relative to the target Reynolds number, giving an overall formal cost of O(log(Re)). In plane channel flow, a model trained at Reτ=1000 corrects the wake-layer error of the baseline model and retains the improvement at Reτ=5200. In the periodic hill, a model trained at Reb=5600 is tested at Reb=10595, 19000, and 37000. The constrained formulation preserves separation and recovery behavior as Reynolds number increases, yields the lowest root-mean-square error across all tests, and exhibits nearly Reynolds-number-independent error, indicating robust extrapolation.