A novel direct forcing approach for the efficient simulation of wave loads on offshore wind substructures with REEF3D::NHFLOW

Predictions of wave forces on coastal technical structures, such as offshore wind energy foundations, are essential for the reliable design of these installations. However, existing numerical models with the required accuracy are computationally demanding, limiting their applicability when it comes to large domains with complex bathymetries and realistic sea states. In this article, a direct forcing extension of the non-hydrostatic, phase-resolving wave model REEF3D::NHFLOW is presented, allowing the accurate prediction of wave forces on structures with significantly reduced computational cost compared to established two-phase CFD solvers. REEF3D::NHFLOW is based upon a Godunov-style finite-volume approach with inherent shock-capturing properties, ensuring robust performance for steep and breaking wave conditions. High-order accuracy is achieved through the use of an HLL-type Riemann solver paired with fifth-order WENO reconstruction, while dispersion characteristics are enhanced by a projection-based pressure-correction strategy. Free-surface evolution is handled using a σ -coordinate grid with dynamic mesh adjustment. The model has been successfully used for simulating wave fields across extensive oceanic and coastal regions. The capability to incorporate solid structures that are not aligned with the computational grid is introduced by embedding a forcing contribution into the governing equations, activated via the direct-forcing immersed boundary method (DF-IBM) applied to either the Euler or Navier–Stokes formulations. The immersed boundary interface is identified with an efficient ray-casting algorithm. A related Heaviside function determines where the direct forcing operates. Comparison against four laboratory experiments shows that the proposed method reproduces wave–structure interaction with high accuracy, while offering substantial computational advantages over traditional two-phase CFD solvers.