VMS-Stabilized Reduced-Order Modeling for High-Fidelity Wind Field Prediction Around Wind Turbines in Complex Terrains

  • Bayona-Roa, Camilo (Pontificia Universidad Javeriana)
  • Vega-Sánchez, Sofia Margarita (Pontificia Universidad Javeriana)
  • Aparicio-Zarate, Juan David (Pontificia Universidad Javeriana)

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Site-specific assessments for small-scale wind turbines (SWTs) in complex environments require high-fidelity predictions, especially in low-wind regions where commercial tools relying on simplified flow representations systematically underperform. While Full-Order Models (FOMs) based on Computational Fluid Dynamics (CFD) offer the requisite precision, their extreme computational cost makes routine micro-siting impractical. To address this, we propose a Reduced-Order Model (ROM) that maintains the physical rigor of the incompressible Navier-Stokes equations at a fraction of the computational demand. Our methodology utilizes the Finite Element Method (FEM) augmented with a Variational Multiscale (VMS) framework [1]. The VMS approach explicitly decomposes the continuous solution space into resolved scales and unresolved subgrid scales ($\mathcal{Y} = \mathcal{Y}_h \oplus \tilde{\mathcal{Y}}$). This provides natural numerical stabilization for convection-dominated regimes and a consistent theoretical foundation for implicit turbulence modeling without ad-hoc closures both in online ROM and offline FOM phases. During the offline phase, a global reduced basis is extracted from high-fidelity VMS-FOM snapshots using Proper Orthogonal Decomposition (POD), a reduction strategy we have successfully extended to highly parameterized, thermally coupled, and non-Newtonian flow scenarios [2, 3, 4]. In the online phase, the governing equations are projected onto this reduced subspace, enabling rapid resolution. Beyond its mathematical robustness, this work will show to the audience a direct technological applicability for planetary-scale wind assessment. The computational framework is designed to integrate diverse, multi-source boundary conditions—including GIS-based topography and meteorological tower data—to construct highly accurate, site-specific domains. By executing the online ROM phase efficiently on standard personal computers, this offline-online structure bridges the gap between advanced numerical mathematics and practical engineering needs, empowering reliable wind resource evaluation at any geographic location.