Multi-fidelity turbulence model discovery for steady RANS via partially converged CFD-in-the-loop evaluations

This paper presents an iteration-based multi-fidelity framework to reduce the computational cost of CFD-in-the-loop turbulence model discovery for steady Reynolds-averaged Navier–Stokes (RANS) simulations. The framework builds on tensor-based gene expression programming (TB-GEP), which generates symbolic turbulence models embedded directly into CFD solvers and evaluated a posteriori during training. Instead of advancing every newly generated candidate to a practical high-fidelity endpoint, the framework first evaluates all candidates at a partially converged CFD state. The resulting fitness estimates guide multi-objective preselection of a small subset of promising candidates for continuation to the high-fidelity endpoint. The framework is applied to coupled Reynolds-stress anisotropy and turbulent kinetic energy production corrections for rectangular-duct flow. This is a challenging benchmark in which baseline k – ω SST fails to predict Prandtl’s secondary flow of the second kind. Compared with conventional single-fidelity CFD-in-the-loop training, the proposed approach reduces nominal search-stage solver work by approximately 71% to reach the same training-score target. The representative coupled model improves secondary-flow and turbulent kinetic energy predictions relative to baseline SST in all six test duct cases. The results support partially converged CFD states as a practical source of fitness guidance for more efficient turbulence model discovery in the steady RANS configurations considered.