A three-dimensional arbitrary Lagrangian–Eulerian Petrov–Galerkin finite element model for fully nonlinear free-surface waves

Abstract

A three-dimensional numerical model based on the incompressible Navier–Stokes equations is developed to simulate fully nonlinear water wave propagation problems. The Navier–Stokes equations are solved using the Arbitrary Lagrangian–Eulerian scheme (ALE) and the Petrov–Galerkin Finite Element Method (PG-FEM). A fractional step method is used in the time discretization, where the convection and diffusion terms are separated from the pressure terms when solving the momentum equations. A damping layer is set in front of the outgoing boundary for absorbing the outgoing waves. The model is validated against a series of experimental data, including wave propagation over a submerged bar, wave propagation over a semicircular shoal and wave propagation over a submerged vertical breakwater. The good agreement between the numerical results and experimental data demonstrates the capacity and the accuracy of the model for simulating wave propagation over uneven seabed and wave interaction with submerged structures.