A NONLINEAR AND DISPERSIVE 3D MODEL FOR COASTAL WAVES USING RADIAL BASIS FUNCTIONS

Abstract

Accurate wave propagation models are required for the design of coastal structures and the evaluation of coastal risks. Nonlinear and dispersive effects are particularly important in the nearshore environment. Two-dimensional cross-shore (2DV) wave models can be used as a preliminary step in coastal studies, but 3D models are needed to capture fully the effects of alongshore bathymetric variations, variable wave incidence, the presence of coastal or harbor structures, etc. Yates and Benoit (2015) developed a numerical model based on fully nonlinear potential flow theory. By assuming non-overturning waves, the kinematic and dynamic free surface boundary conditions are expressed as evolution equations of the free surface elevation and velocity potential, following Zakharov (1968). At each time step, the free surface vertical velocity is estimated by solving the Laplace equation for the velocity potential in the domain. Following Tian and Sato (2008), a spectral approach is used to expand the velocity potential in the vertical as a linear combination of Chebyshev polynomials. The accuracy of the 2DV model was validated with several non-breaking experimental test cases (Benoit et al., 2014; Raoult et al., 2016). Here the model is extended to 3D using scattered nodes (for flexibility) to discretize the horizontal domain. Spatial derivatives are estimated at each node using a linear combination of the function values at neighboring points using Radial Basis Functions (RBF) (Wright and Fornberg, 2006). The accuracy of the method depends on the number of neighboring nodes (Nsten) and the chosen RBF type (e.g. multiquadric, Gaussian, polyharmonic spline (PHS), thin plate spline, etc.), with associated shape factor C for some of them.