Consistent reduced order modeling for wind turbine wakes using variational multiscale method and actuator line model

We present a consistent ALM-VMS-ROM framework for the efficient and accurate reduced-order modeling (ROM) of wind turbine wakes. The method leverages a finite element discretization with a POD-Galerkin approach for constructing ROM. A reduced basis space includes the projection of VMS stabilization terms, ensuring numerical stability without requiring additional stabilization techniques. To further enhance computational efficiency, we implement a mesh-based hyper-reduction technique for predicting the wake behavior behind the NREL 5 MW wind turbine, where the rotor is modeled using the Actuator Line Method (ALM). Using fine-mesh snapshots, the wake dynamics are accurately reconstructed with only 10 POD modes, while employing a coarse mesh in both the reconstruction and prediction phases. The proposed framework achieves a computational speed-up of nearly 13xcompared to the fine-mesh full-order model (FOM), while maintaining high accuracy in power production and wake deficit predictions up to 7D downstream.