PhD Defense Nikita Kozak “Toward Generalizable Data-Driven Turbulence Models via Equivariant Learning”

Turbulence at engineering Reynolds numbers spans too many scales to resolve directly, forcing computational fluid dynamics (CFD) to trade fidelity against computational cost. Large-eddy simulation (LES) resolves the energy-containing scales and is accurate, but remains too expensive for routine design use. Reynolds-averaged Navier–Stokes (RANS) instead solves only the mean flow, and the averaging that makes it affordable leaves an unclosed term, the Reynolds stress, representing momentum transport by the discarded fluctuations. Classical closures prescribe this stress through calibrated constitutive relations with strong assumptions that often break in practical engineering flows and give no warning when they fail. Data-driven closures instead learn the stress relation from high-fidelity data, but they must generalize beyond their calibration cases and ultimately operate within a CFD solver. In practice most data-driven closures are trained on narrow datasets and evaluated offline, so they neither demonstrate generalization nor connect to the solver they are meant to serve. This dissertation addresses both requirements through two tasks: RANS2LES, which predicts LES Reynolds stresses from RANS fields, and ML2CFD, which couples those predictions back into a RANS solver.