A Stabilized Finite Element Framework for Physics-Enhanced RANS Modeling and Optimization in Wind Farm Simulations

We present a framework for unsteady Reynolds-Averaged Navier–Stokes (RANS) simulation tailored to wind energy applications. The formulation incorporates a suite of physical modeling capabilities critical for simulating physically representative atmospheric boundary layer flows, including Coriolis forcing, thermal convection, one-equation turbulence models, and surface flux parameterization through Monin–Obukhov similarity theory (MOST). Central to our formulation is a stabilized finite element method designed to ensure robustness across a wide range of flow conditions. We adopt residual-based stabilization (SUPG/PSPG) and introduce a novel formulation of the stabilization parameter that responds to transient flow changes and local mesh anisotropies. This design seeks to improve numerical stability by applying stabilization more selectively, helping to limit excessive artificial diffusion. We leverage the WindSE framework — an open-source platform for wind farm simulations built on FEniCS that features automatic differentiation — as a foundation for these advancements. By improving the underlying physical modeling and numerical stabilization, we enhance the fidelity of the solver outputs upon which gradient-based optimization relies, enabling more physics-informed decision-making across various optimization objectives — including turbine layout, model parameter calibration, and inference of physical parameters.