Modeling fully nonlinear shallow-water waves and their interactions with cylindrical structures

Introduction of a time-accurate stabilized finite-element approximation for the numerical investigation of fully nonlinear shallow-water waves is presented in this paper. To make the time approximation match the order of accuracy of the spatial representation of the triangular elements by the Galerkin method, the fourth-order time integration of implicit multistage Padé method is used for the development of the numerical scheme. The Streamline-Upwind Petrov–Galerkin (SUPG) method with cross-wind diffusion is employed to stabilize the scheme and suppress the spurious oscillations, usually common in the numerical computation of convection dominated flow problems. The performance of numerical stabilization and accuracy is addressed. Numerical results obtained for cases representing propagation of solitary waves, collisions of two solitary waves, and wave-structure interactions show fairly good agreement with experimental measurements and other published numerical solutions. The comparisons between results from present fully nonlinear wave model and weekly nonlinear wave model are presented and discussed.