Development and validation of a 3D RBF-spectral model for coastal wave simulation

With the objective of simulating wave propagation in the nearshore zone for engineering-scale applications, a two dimensional (2DV) model based on the Euler–Zakharov equations [73,54] is extended to three dimensions (3D). To maintain the flexibility of the approach with the goal of applying the model to irregularly shaped domains, the horizontal plane is discretized with scattered nodes. The horizontal derivatives are then estimated using the Radial Basis Function-Finite Difference (RBF-FD) method, while a spectral approach is used in the vertical dimension. A sensitivity analysis examined the robustness of the RBF-FD approach as a function of RBF parameters when estimating the derivatives of a representative function. For a targeted stencil size between 20 and 30 nodes, Piecewise-Smooth (PS) polyharmonic spline (PHS) functions are recommended, avoiding the use of Infinitely-Smooth (IS) RBFs, which are less appropriate for the desired applications because of their dependence on a shape parameter. Comparisons of simulation results to observations from two wave basin experiments show that nonlinear effects induced by complex bottom bathymetries are reproduced well by the model with the recommended RBF approach, validating the use of this method for 3D simulations of wave propagation.